Preheat oven to 400F.
Brush all the peppers with olive oil and place on a baking sheet.
Bake until the skin becomes black and blistered-- about 10 minutes per side.
Remove from the heat and let cool completely.
Remove the stem and seeds and dice the peppers.
In a large saucepan set over medium heat, add the butter and allow it to melt. Add the flour and whisk to combine-- the mixture will thicken and start to bubble. Allow it to cook for one minute.
Add the milk and whisk until no lumps remain. Allow the mixture to thicken, stirring often, until it can coat the back of a spoon-- about 3 minutes.
Reduce the heat to low and add in the mozzarella and white cheddar cheese in small amounts until fully melted. Be sure to continuously stir at this step so the cheese melts smoothly.
Stir in the garlic, onion, chili, and cumin powders.
Transfer to a serving dish and top with the chopped roasted poblano peppers. Enjoy while warm.
Store any leftover queso in an airtight container in the fridge for up to three days.