Rub steaks with chopped thyme, salt, and pepper.
Melt butter in a large skillet over medium heat; add oil. Add steaks, and cook 1 to 3 minutes on each side or to desired degree of doneness. Remove steaks, and keep warm; reserve drippings in skillet.
Stir wine and consomme into drippings; increase heat to high. Cook, stirring often, until reduced to 1/2 cup. Stir in half-and-half, and cook, stirring constantly, until reduced to 1/2 cup or desired consistency. Keep warm.
Snap off tough ends of asparagus; remove scales with a vegetable peeler, if desired. Cut spears in half, and place in a steamer basket over boiling water. Cover and steam 8 minutes or until crisp-tender. Top steaks with asparagus, and sprinkle with cheese.
Broil 6 inches from heat (with electric oven door partially open) 2 minutes or until cheese melts. Serve immediately with sauce.