Roast poblano peppers on a comal or cast-iron skillet over medium-high heat until blistered and blackened on all sides. Transfer to a plastic bag, seal, and let steam for 5–10 minutes, then uncover and let cool.
Preheat oven to 350°F.
Once peppers are cool enough to handle, peel off the loosened skin, remove stems and seeds, and slice into thin strips (rajas). Wear gloves if needed.
Heat a large nonstick pan over medium heat. Remove the casing from the chorizo and cook, breaking it apart, until browned and fully cooked, 6–8 minutes. Add a little oil if needed.
Stir in onion and garlic; cook until softened, about 3–4 minutes. Remove from heat and mix in the poblano strips. Combine the Monterey Jack and Oaxaca cheese until well incorporated.
Lightly grease a 6x9-inch baking dish. Layer one-third of the cheese, half the chorizo mixture, another third of the cheese, the remaining chorizo, and finish with the last third of cheese.
Bake for 15 minutes, or until melted through. Switch oven to broil on high and brown the top, about 2 minutes, watching closely.
Remove from oven and serve with flour tortillas.