Heat oven to 450°F. In 8-inch skillet, heat oil over medium-low heat. Add garlic to oil; cook 5 to 7 minutes, tossing only once, until golden brown. Drain garlic through strainer (reserve oil to brush on steaks); cool. In small bowl, mash cooled garlic roughly with a fork into a chunky paste. Add thyme to garlic paste, mashing until well blended yet still chunky. Stir in mustard; set aside.
Heat 12-inch skillet over high heat until hot. Season steaks with salt and pepper; drizzle both sides of steaks with reserved oil. Add steaks to hot skillet, browning on both sides until crust forms. Place on cookie sheet; spread garlic-mustard mixture over tops of steaks.
In medium bowl, toss together bread crumbs and Parmesan cheese. Top steaks generously with bread crumb mixture, spreading to edges. Bake uncovered 25 to 35 minutes or until instant-read thermometer inserted in center reads 135°F for medium-rare or 150°F for medium (temperature will continue to rise about 10°F upon standing).
Meanwhile, make beef gravy. In same 12-inch skillet, cook flour and butter over medium heat 3 to 4 minutes, stirring constantly, just until a blonde roux forms. Stir in broth. Heat to boiling over high heat, stirring constantly. Reduce heat and simmer, stirring constantly, just until thickened.
Allow steaks to rest a few minutes before slicing. Serve gravy over steaks. If desired, serve with mashed potatoes.