Pick through the dried beans and remove any debris or damaged beans. Rinse well under cold water. Add the beans to a pot with the water, halved onion, smashed garlic, and bay leaf. Bring to a boil, then reduce immediately to a gentle simmer. Cook uncovered or partially covered for 1 hour 45 minutes to 2 hours, stirring occasionally and topping up with hot water if needed, until the beans are fully tender. The beans must be completely soft before you move on. A bean should mash easily between your fingers with no chalky centre. Add the 10g salt only in the last 20–30 minutes of cooking. Remove and discard the onion halves, garlic, and bay leaf once done. Before draining, reserve at least 500ml of the cooking liquid. This liquid is essential for getting the right creamy texture later. Adding salt only toward the end of this long simmer, rather than from the start, protects the beans' skins from toughening — salt introduced too early can interfere with how evenly the beans soften over such an extended cook.

In a wide skillet or sauté pan, heat the lard over medium heat. Add the finely diced onion and cook for 5–7 minutes, stirring regularly, until soft and lightly golden at the edges. Add the minced or grated garlic and cook for 30–45 seconds, just until fragrant. If using cumin, add it now and stir for a few seconds. The onion should be soft and sweet, not browned deeply, and the garlic should not darken or it will bring bitterness. Cooking the onion until only softened and lightly golden, stopping well short of deep browning, builds a sweet aromatic base without introducing the sharper, more caramelised notes that would compete with the beans' own flavour once everything is combined.

Add the cooked beans to the pan with the aromatics. Start with about 700–750g cooked beans, which should be roughly the full cooked yield from 400g dried beans. Add about 250ml of reserved bean cooking liquid and stir. Mash the beans with a potato masher or the back of a sturdy spoon while they fry gently in the fat. Continue cooking and mashing for 8–12 minutes, adding more bean liquid as needed. The goal is a creamy mash with a little rustic texture — not fully puréed, but not chunky either. Season with the additional ½ tsp salt if needed and black pepper to taste. The beans should look glossy, cohesive, and spreadable. When dragged with a spoon, they should hold a soft ridge for a moment before relaxing back down. If they look stiff or dry, add more bean liquid a little at a time. Mashing the beans directly in the pan while they're actively frying in the fat, rather than mashing them separately beforehand, is what allows the fat and starchy cooking liquid to properly emulsify into the bean mash — that direct, simultaneous contact is what produces the glossy, cohesive finish this recipe depends on.

Lower the heat and continue stirring for another 1–2 minutes to let everything emulsify. Taste and adjust salt. If serving immediately as a bowl or side dish, spoon the beans into a serving bowl and create a broad swirl on top with the back of a spoon. The final texture should be looser than you think if they are being held for a few minutes, because refried beans thicken quickly as they sit. Refried beans' starch content continues absorbing residual liquid and firming up even after they're pulled from the heat — deliberately erring toward slightly looser than the ideal serving texture accounts for that continued thickening between the pan and the table.

Top with crumbled cotija, drizzle over the crema in thin white threads, and scatter a few cilantro leaves if desired. Serve warm. For burritos or rice bowls, use about ⅓ to ½ cup per serving. These finishing touches are deliberately simple and added only at the very last moment — cotija's texture, crema's drizzle, and cilantro's freshness are all best preserved by staying distinct on top of the hot beans rather than being stirred through and losing their individual character.