This recipe is different than others. The recipe traditionally calls for 2 strips of proscuitto rolled into each chicken breast, but I prefer to omit it and thought this dish was still superb. Asadero cheese, sometimes labelled Chihuahua or Oaxaca cheese, is a white cow's milk cheese with good melting properties. It can be found in Latin markets and most cheese shops. The Gourmet Sleuth website states that adequate substitutes are Fontina or Monterey Jack (which Monterey Jack is what I used but only because it's much easier to find).
Place chicken breasts between 2 pieces of plastic wrap and, using the flat end of a meat mallet, flatten it to about 1/4 inch thickness. Repeat with remaining chicken breasts. (I skipped this step by purchasing thinly cut chicken breasts.).
Place chicken on clean surface and sprinkle the top of each flattened chicken breast with 1/3 cup of the grated cheese. Starting with the long side, roll each breast into a tight cylinder. (I secured the rolled chicken breasts with toothpicks, but it wasn't included in the original recipe instructions.).
Place each rolled chicken breast, seam side down and ends tucked under, into a 9x13-inch baking dish. The rolls should be touching. Cover and refrigerate until needed.
In a food processor fitted with a metal blade, combine the chiles, heavy cream, sour cream, and salt. Process 2 to 3 minutes or until thoroughly blended, stopping once or twice to scrape the sides.
Place chile mixture in 4-quart saucepan, add the chicken broth, and place on stove over medium heat. Bring to gentle simmer and cook, uncovered and stirring occasionally, until the mixture reduces slightly and thickens enough to coat the back of a spoon, about 20 minutes.
Pour the sauce mixture over the prepared chicken breasts and top with the remaining grated cheese. Bake at 350° for 50 to 60 minutes, or until the chicken is cooked thoroughly and the cheese is slightly browned and the sauce is bubbling. Remove from the oven, and let stand 5 minutes before serving.
Using a spatula, transfer the chicken to warmed dinner plates and spoon sauce over each serving. Serve immediately.