In a large skillet, melt the butter or lard over medium heat. Add the chopped onion (or scallions) and achiote powder/oil. Cook for 3–5 minutes until the onion is soft and the achiote releases its color.
Add the minced garlic and a pinch of salt. Cook for another minute until the garlic is fragrant.
Add the cooked and drained mote corn to the skillet and mix well with the refrito.
Cook for about 2 minutes to allow the corn to absorb the flavors.
Pour in the milk (if using) and cook until the liquid is almost fully absorbed. This adds a creamier texture to the dish.
Whisk the eggs in a bowl with salt and black pepper.
Pour the eggs over the corn mixture in the skillet. Reduce the heat and cook, stirring continuously, until the eggs are set and creamy, which takes approximately 3–5 minutes.
Remove from heat. Fold in the shredded/crumbled cheese and the chopped cilantro/parsley. Don't skimp on the cheese – Mote Pillo should be hearty and cheesy.