Set a 10- to 12-inch skillet with a lid over medium heat.

Add the olive oil to the skillet and heat it until it looks loose and shiny, about 30 seconds.

Add the chopped poblano and the white parts of the scallions to the skillet. Add a small pinch of the salt and cook, stirring often, until the vegetables soften, 4 to 5 minutes.

Add the garlic, cumin, and smoked paprika to the skillet. Stir for about 30 seconds, just until the garlic smells fragrant.

Add the frozen corn to the skillet. Stir well so the kernels are coated with the oil and spices.

Cook the corn, stirring every minute or so, until it is no longer icy and is hot all the way through, 3 to 4 minutes.

Pour the milk into the skillet and let it come to a gentle simmer.

Add the cream cheese cubes and 1/2 teaspoon of the salt to the skillet. Stir until the cream cheese melts and the corn mixture looks creamy, 2 to 3 minutes.

Add a few grinds of black pepper and stir in half of the Monterey Jack cheese until it melts into the corn mixture.

Use the back of a spoon to make 6 shallow wells in the corn mixture so the eggs have a place to sit.

Crack 1 egg into a small bowl, then slide it into 1 well in the skillet.

Repeat with the remaining eggs, placing 1 egg into each well.