Preheat broiler to high. Place poblanos in metal baking pan or on rimmed baking sheet. Place under broiler, flipping once, until skin of peppers is completely blistered and blackened, about 15 minutes. Remove to bowl, cover and let rest 15 minutes. When peppers are cool enough to handle, peel away skin and discard. Cut chiles open and remove seeds and ribs (or leave them in for an extra spicy dish!). Coarsely chop peppers; set aside.
Bring large pot of water to boil. Add pasta and cook according to package directions until al dente. Drain pasta well and leave in colander; set aside.
Return pot to burner over medium heat and melt butter. Add cumin, paprika and garlic powder and cook just until fragrant, about 30-60 seconds. Return pasta to pot and add shredded cheeses, Greek yogurt and milk. Stir in chopped poblano peppers. Season generously to taste with salt and pepper. Stir until cheese is melted and smooth. Taste and adjust seasonings if necessary. Serve immediately.