First, make the marinade for the chicken: Combine the olive oil, lime juice, cumin, salt, pepper, chipotle peppers and garlic in a blender and mix until totally pureed. Pour into a large resealable plastic bag with the chicken breasts. Seal the bag, smush it around to coat the chicken and place it in the fridge to marinate for at least 4 hours (overnight if possible).
After the chicken has marinated, roast the poblano chiles one-by-one over the flame of your stovetop, using metal tongs to hold them, until the skin is totally charred. (If you don't have a gas stove, you can use an outdoor grill OR place them on a baking sheet directly under your oven's broiler.) When the skin is totally blackened, place the chiles in a large resealable plastic bag and seal the bag to allow the chiles to sweat for a good 20 minutes. Remove the chiles and use a knife to scrape off most of the blackened skin. Slice the chiles in half lengthwise, and scrape out the seeds and membranes. Lay out the chile halves so they'll be ready for the next step.
Preheat a grill pan to medium-high heat (or use a skillet). Grill the chicken (or saute in the skillet) for 4 minutes on the first side. Turn the chicken over and lay 2 chile halves and a nice slice of cheese on the cooked side of each piece. Turn the heat to medium low and allow the chicken to finish cooking until it's totally done in the center, 4 to 5 minutes. The cheese should melt on its own; if it needs a little help, invert an iron skillet over it (or put the lid on the skillet, if using). Serve!
You can also use any marinade you'd like, homemade or store-bought, for the chicken! Anything works.
Recipe courtesy of Ree Drummond