Place the chicken in a medium saucepan with the salt, a few grinds of black pepper, the halved onion, garlic, bay leaf, and water or light stock. Bring to a gentle simmer over medium heat. Once the liquid starts moving, reduce the heat so the chicken barely simmers rather than boils aggressively. Cook for 16–20 minutes, depending on thickness, until the chicken is just cooked through and tender. Transfer the chicken to a plate and let it cool just enough to handle. Reserve about 300ml of the cooking liquid — this is useful for keeping the mole fluid and the chicken moist. Shred the chicken into short, fine strands rather than large chunks. The chicken should shred easily and stay juicy. If it is boiled too hard, it will become tight and dry, which is noticeable in a simple preparation like enmoladas. A genuinely gentle simmer keeps the chicken's own moisture intact through cooking — that moisture matters directly here since this dish has so few components that any dryness in the chicken has nowhere to hide.

Add the sesame seeds to a dry skillet over medium-low heat. Toast, stirring constantly, for 2–3 minutes until lightly golden and fragrant. Transfer immediately to a bowl so they do not continue cooking in the hot pan. They should smell nutty and look pale golden, not dark brown. Burnt sesame will read bitter against the mole. Removing the seeds from the hot pan the instant they're toasted protects them from continuing to darken under the pan's own residual heat, even once the burner is off.

Place the mole poblano in a wide saucepan or deep skillet over medium-low heat. If needed, add the tablespoon of oil or fat first, then add the mole. Warm it slowly, stirring often. Add some of the reserved chicken cooking liquid, starting with about 150ml, and stir until the sauce becomes smooth, glossy, and fluid enough to coat the tortillas generously. Add more broth a little at a time if needed. The final texture should be thick enough to cling well but loose enough to spread and pool around the enmoladas without feeling heavy or muddy. Taste and adjust seasoning if needed. Properly heated mole should fall from the spoon in thick ribbons, not sit like stiff paste. If it becomes too thick, it will smother the tortillas unpleasantly rather than coat them elegantly. Using the chicken's own reserved cooking liquid to loosen the mole, rather than plain water, ties genuine savoury flavour directly back into the sauce rather than simply diluting it.

Add 2–3 spoonfuls of the warm mole or a small splash of reserved broth to the shredded chicken and toss lightly. This should not turn the filling saucy — it is just to keep the chicken moist and flavorful inside the tortillas. The chicken should be lightly seasoned and juicy, not wet. A soaked filling can make the tortillas tear and the finished dish heavy. Tossing the chicken with only a small amount of mole, rather than a generous helping, gives it real flavour and moisture without introducing enough liquid to compromise the tortilla's structure once it's filled and folded.

There are two classical approaches here: lightly fry the tortillas so they stay flexible and flavorful, or warm them on a dry skillet/comal if you want a lighter version. For the most traditional texture, lightly fry them. Heat a thin layer of neutral oil in a skillet over medium heat. Fry the tortillas one at a time for about 8–12 seconds per side — just enough to soften them and lightly blister them, not enough to crisp them. Transfer to a tray lined lightly with paper towel or a clean cloth. If not frying, warm the tortillas on a hot dry skillet until soft and pliable. Keep the tortillas covered with a towel so they stay warm and flexible. The tortillas must stay soft and bendable. If they crisp, they will crack when folded. If they sit too long uncovered, they will dry out and tear. This genuinely brief fry, just seconds per side, is calibrated specifically to soften and lightly blister the tortilla without pushing it toward the crispness that would make folding it impossible without cracking.

Working while everything is warm, place a portion of shredded chicken down the center of each tortilla — about 55–60g per tortilla. Fold each tortilla in half, or roll loosely if you prefer that shape. Enmoladas are commonly folded in half rather than tightly rolled. Arrange 3 filled tortillas per plate, slightly overlapping, or place all 12 in a large serving platter if serving family-style. Do not overfill. Too much chicken makes the tortillas burst and prevents the mole from coating them neatly. Keeping the fill to this specific, moderate amount protects the tortilla's structural integrity through both the fold and the subsequent mole coating — an overfilled tortilla has considerably less margin before it tears or splits open.

Spoon the warm mole generously over the folded tortillas until they are fully covered. The tops should be completely blanketed, with a little extra mole pooling underneath and around them. Drizzle the crema across the top in thick lines. Scatter over the crumbled queso fresco and the toasted sesame seeds. Finish with the very thin white onion rings. Serve immediately while hot. The mole should still be glossy and hot when spooned over. If it sits too long and thickens, loosen it again before plating so the finish stays smooth and elegant rather than clumpy. Slicing the onion garnish especially thin, rather than a standard cut, is what lets it complement the mole with a light, sharp accent rather than dominating each bite with raw onion intensity.