Preheat the oven to 450°F. Line a baking sheet with foil.
Cut the poblano peppers in half and remove the seeds. Place them cut-side down on the prepared baking sheet.
Drizzle the peppers with olive oil and season with salt and black pepper.
Bake for 15 minutes, until the skins are slightly blackened. Let cool for 5 minutes, then remove the skins and finely dice the peppers.
Finely dice the tomatoes.
Combine the American cheese, white American cheese, Monterey Jack cheese, and heavy whipping cream in a saucepan. Cook over low heat, stirring often, until melted and smooth.
Stir in the paprika, cayenne pepper, garlic powder, diced poblano peppers, and tomatoes. Cook for a few minutes, until combined and heated through.
Serve warm.
Notes
If you want a spicier Queso, add 1 more poblano peppers into the queso to add more heat.Store the leftovers in an air tight container in the refrigerator for up to 5 days. You may have to add more cream or milk when reheating as the queso will thicken as it sits.