Slit chiles lengthwise on one side. Remove seeds and drain. Slice Monterey Jack cheese into 1/4-inch thick slices and place inside chiles. Place stuffed chiles in an ungreased 3 quart baking dish. Mix eggs, milk, flour, salt and pepper well, and pour over chiles. Sprinkle top with grated Cheddar. Bake uncovered at 350 degrees for 45 minutes.