Start by washing and dicing your poblano peppers. Heat the olive oil in your medium saucepan over medium heat, then add the diced peppers. Sauté for about 5-7 minutes until they're tender and slightly charred.
In the same saucepan with the sautéed peppers, add the butter and let it melt. Once melted, sprinkle in the all-purpose flour and whisk continuously for about 1-2 minutes to create a roux that helps thicken your queso.
Gradually pour in the whole milk while continuing to whisk. Keep stirring until the mixture is smooth and starts to thicken, about 3-5 minutes.
Lower the heat and add in the white American cheese and mozzarella cheese. Stir until the cheeses are completely melted and the dip is smooth. Turn up the heat slightly if needed but be careful not to let it boil.
Add the garlic powder, onion powder (if using), chili powder, and ground cumin. Stir to combine. Taste your queso and adjust the seasonings if needed.
Remove the saucepan from the heat. Transfer your queso blanco to a serving bowl and top with chopped cilantro, additional diced poblanos, or jalapeños. Serve immediately with tortilla chips, veggies, or drizzled over tacos.