Preheat the broiler to high. Broil the poblanos on a pan until charred on all sides, 12 to 15 minutes. Place in a paper bag and let cool for 10 minutes. Peel, seed and chop.
While the chiles cook, season the chicken with the chili powder, cumin and salt and pepper to taste.
In a large nonstick skillet, heat 1 tablespoon EVOO, 1 turn of the pan, over medium-high heat. Add the chorizo and cook until the fat renders, 2 minutes. Add the sweet potatoes and yellow onion and arrange evenly in the skillet. Season with pepper and cook for 10 minutes. Flip and cook, pressing with a spatula, until crisp, 10 minutes more.
Preheat a grill pan over medium-high to high heat. In a saucepan, heat 1 tablespoon EVOO, 1 turn of the pan, over medium heat. Add the red onion and garlic; cook until softened, 8 minutes. Add the tomatoes, reserved poblanos and salt and pepper to taste; keep warm.
Coat the chicken with the remaining 1 tablespoon EVOO and grill on the hot grill pan for 5 minutes on each side.
Pile the sweet potato mixture on 4 plates, slice the chicken breasts and arrange over the potatoes. Top with the poblano-tomato sauce.