At the White Gull Inn in Fish Creek, Wisconsin, cheddar and mushrooms flavor indulgent steaks.
Melt butter in skillet. Add green onion, mushrooms and thyme. Cook, uncovered, 3 to 5 minutes, or until onions are tender, stirring occasionally. Remove from heat. Remove about one third of the mushroom mixture to serve over the finished steaks. Set aside. Stir cheese into remaining mushroom mixture.
Cut a 3-inch-wide pocket in the side of each tenderloin filet, cutting to but not through the other side. Spoon half the cheese-mushroom mixture into each pocket. Sprinkle meat lightly with salt and pepper. Wrap 2 slices of bacon around each steak; secure with wood toothpicks.
Place on unheated rack of broiler pan. Broil 4 to 5 inches from heat 20 to 24 minutes, or until an instant-read thermometer inserted in center of meat and stuffing registers 145° for medium-rare or 160° for medium, turning the steaks halfway through cooking time. Transfer to plates; top with reserved mushroom mixture.
Remove and discard stems before slicing shiitake mushrooms.