Preheat oven to 425°F. Stir together 3 tablespoons mustard, salt, pepper, thyme and rosemary in small bowl. Rub mustard mixture over beef.
Heat large nonstick skillet over medium-high heat. Add oil and beef to skillet. Cook beef on each side 2 minutes, until lightly browned. Remove to a baking dish and bake until internal temperature reads 135°F, about 40 to 50 minutes.
Combine:
Pour beef broth into skillet and stir to remove browned bits. Simmer 10 minutes; set aside and keep warm. Use a slotted spoon to remove any large bits, if desired.
Remove beef from oven and cover tightly with foil. Rest 15 minutes, until internal temperature reaches 145°F for medium rare.
Create:
Place bun halves on baking sheet. Spread each evenly with butter. Bake 10 minutes, until lightly toasted.
Spread remaining mustard evenly on bottom buns.
Use a sharp knife to shave beef as thinly as possible. Divide beef evenly onto bottom buns.
Top with cheese and top buns. Serve with warm au jus for dipping.