Light your grill, setting up one side for high heat and one for medium heat.
Grate cheeses with a box grater.
Rub poblano peppers with olive oil and a pinch of salt. Place peppers on the grill over high heat and char the entire surface of the pepper, flipping often.
Place a saucepan over low heat on grill and melt butter. Whisk flour into melted butter to make a roux, cook over medium heat for 3 minutes.
Add milk and cream to the roux. Continue whisking 2-3 minutes. Add in cheese, chilies, salt, pepper, and garlic powder. Cook for additional 5 minutes, until mixture has melted smooth. Reduce heat to low and keep warm.
Remove peppers from grill, peeling off the outer skin and removing seeds.
While peppers are cooling, place burger patties over medium direct heat, cook 3-4 minutes per side.
Place burger on bun, top with pepper, queso sauce, pico de gallo, and cilantro.
Poblano Burgers with Queso Fresco https://www.grillseeker.com/poblano-burgers-with-queso-fresco-recipe/