PLACE bread in single layer in greased 8-inch square baking dish.
BEAT eggs, milk and thyme in medium bowl until blended; pour over bread.
SPRINKLE with bacon. REFRIGERATE, covered, at least 30 minutes or as long as overnight.
HEAT oven to 350°F. REMOVE strata from refrigerator; uncover and let stand while oven heats. BAKE in center of 350°F oven 30 minutes. SPRINKLE with cheese. BAKE until puffed, golden and firm in center, about 5 minutes longer.