ADD BUTTER TO A LARGE SKILLET AND ALLOW TO MELT. ADD THE MUSHROOMS AND ONIONS AND SAUTE 5-7 MINUTES.
SPRINKLE THE FOUR OVER THE MIXTURE AND STIR TO COAT.
ADD CHICKEN BROTH ONE SPLASH AT A TIME, WHISKING AFTER EACH ADDITION, UNTIL THICKENED.
STREAM IN THE HALF AND HALF. STIR TO COMBINE AND SIMMER FOR 6 MINUTES.
REMOVE FROM THE HEAT AND ADD HALF OF THE CHEDDAR AND MONTEREY JACK CHEESE, ALONG WITH THE SALT AND PEPPER.
NOW, ADD THE CHICKEN AND RICE.
TRANSFER MIXTURE TO A PREPARED BAKING DISH.
TOP THE CASSEROLE WITH THE REMAINING CHEESE, COVER WITH FOIL AND BAKE 15-20 MINUTES.