Heat the oven to 220°C / 425°F and line a 12-cup muffin pan with parchment tulip liners or regular muffin liners.

Rub the lemon zest into the granulated sugar with your fingertips until the sugar feels fragrant and slightly damp; this releases the lemon oils for a stronger, cleaner citrus flavor. Roughly chop the pistachios, keeping the pieces small to medium rather than finely ground, and set aside 20 to 30 g for the topping, using the rest in the batter. Avoid over-processing the pistachios; fine crumbs disappear into the batter, while distinct pieces give the visible texture this muffin is known for.

Whisk together the flour, baking powder, baking soda, and salt in a medium bowl, then add the pistachios for the batter and toss to coat, which helps keep them suspended instead of sinking.

Whisk together the lemon sugar and eggs in a large bowl until smooth and slightly thickened, about 30 to 60 seconds. Add the melted butter, oil, sour cream, milk, lemon juice, and vanilla, whisking until fully combined and smooth. The butter should be warm rather than hot; butter that's too hot can seize in the cold dairy or partially cook the eggs.

Add the dry ingredients to the wet ingredients and fold gently with a spatula just until no dry flour remains. The batter should be thick but scoopable; a few small lumps are fine, since overmixing makes the muffins tighter, tougher, and less domed.

Let the batter rest for 10 minutes at room temperature. This short rest hydrates the flour and helps create a higher dome and more even crumb; don't rest much longer than that once the leaveners are active.

Divide the batter evenly among the 12 muffin cups, filling each about 85 to 90% full for a bakery-style shape. Top each muffin with a few chopped pistachios and a light sprinkle of coarse sugar, if using, pressing the topping very lightly so it adheres without sinking.

Bake at 220°C / 425°F for 5 minutes, then, without opening the oven, reduce the temperature to 190°C / 375°F and continue baking for 13 to 17 minutes, until the tops are domed and pale golden to lightly golden-brown, the centers spring back when lightly pressed, and a tester inserted into the center comes out clean or with a few moist crumbs. Avoid testing directly through a nut pocket. The tops should stay fairly light rather than deeply browned, to keep the clean lemon look this muffin is meant to have.

Cool the muffins in the pan for 5 to 8 minutes, then transfer to a rack and cool another 10 to 15 minutes. Serve slightly warm or fully cooled.