Poblano Chicken Guadalajara

4 to 5 boneless, skinless chicken breasts
1/2 cup flour (for dredging)
4 or 5 poblano chiles (Anaheim chiles may be substituted)
1 large onion, cut into 1/2-inch square pieces
6 ounces heavy cream (or half-and-half)
1 cup shredded Monterey jack cheese
4 tablespoons butter
Salt, pepper and cayenne for seasoning

Roast poblano chiles in oven or over direct flame until blackened. Seal chiles in a zip-type bag for a few minutes to loosen skin. When chiles have cooled enough to handle, remove from bag, peel, split and seed the chiles, slicing them crosswise into half-inch wide strips. Set aside.

Season flour with salt, pepper and a dash of cayenne.

Dredge chicken strips in seasoned flour.

Heat butter in skillet until it browns. Watch carefully. DO NOT BURN THE BUTTER.

Saut