Preheat oven broiler.
Heat the butter and oil in a large skillet over medium-high heat; add garlic and chicken and sauté until lightly browned; remove from pan and set aside.
To the same skillet over medium heat, add broth, chilies, mustard and cream; simmer until liquid is reduced and thickened, salt and pepper to taste.
Combine sauce and chicken in a lightly greased METAL baking pan (DO NOT USE GLASS BAKEWARE FOR BROILING!); top with cheese and broil to melt cheese.
*LEANNE’S NOTE: Partially freeze chicken for ease in cutting.