Heat the oven to 425°F. Set out a 10-inch oven-safe skillet; if your skillet cannot go in the oven, set out a 2-quart baking dish instead.

Put the drained pinto beans and drained hominy in a colander if you have not rinsed them yet. Rinse them under cool water and let them drain well.

Pour the olive oil into the skillet and set it over medium heat.

Add the chopped onion to the skillet. Cook, stirring often, until it starts to soften, about 4 minutes.

Add the chopped poblano to the skillet. Cook, stirring often, until the pepper is tender and the onion looks glossy, 4 to 5 minutes.

Sprinkle the cumin, salt, and black pepper into the skillet. Stir for about 30 seconds, just until the spices smell warm.

Pour the salsa verde into the skillet. Stir well and let it come to a gentle simmer.

Turn the heat to low. Add the sour cream to the skillet and stir until the sauce looks smooth and evenly pale green.

Add the pinto beans to the skillet. Stir gently so the beans are coated with the sauce.

Add the hominy to the skillet. Stir again until the mixture is even all the way through.

Stir 1 1/2 cups of the shredded Monterey Jack into the skillet. Keep stirring just until the cheese starts to melt into the sauce.

If you are using a baking dish instead of an oven-safe skillet, transfer the mixture into the dish now. Spread it into an even layer.