Preheat oven to 250°F. Sprinkle steaks on all sides with salt and pepper. Heat oil in heavy large skillet over high heat. Add steaks and sear until brown, about 2 minutes per side. Reduce heat to medium-low. Add 3 tablespoons butter, garlic, thyme, and rosemary to skillet. Cook steaks to desired doneness, turning occasionally and basting with pan juices, about 12 minutes for medium-rare.
Transfer steaks to small rimmed baking sheet and keep warm in oven.
Pour contents of skillet into small bowl. Return 3 tablespoons drippings from bowl to same skillet and place over high heat. Add shallots and sauté 2 minutes. Add Cognac and Port and stir 1 minute, scraping up any browned bits. Add broth and boil until sauce is reduced to 1 cup, about 12 minutes. Whisk in Dijon mustard, then remaining 3 tablespoons cold butter, 1 tablespoon at a time. Season sauce to taste with salt and pepper. Set aside.
Arrange steaks on plates; whisk any accumulated juices from baking sheet into sauce. Spoon sauce over steaks and serve.
