Note: Be sure to brown the edges of the steak to render the fat. You can do this easily by using tongs to hold the steak on its side in the hot pan.
Adjust oven rack to lowest position and heat oven to 200 degrees. Pat steak dry with paper towels and season with salt and pepper.
Heat oil in 12-inch skillet over medium-high heat until just smoking. Brown steak all over, 10 to 12 minutes. Transfer steak to wire rack set in rimmed baking sheet. Roast until meat registers 120 to 125 degrees (for medium-rare), 25 to 30 minutes. Transfer steak to cutting board, tent loosely with aluminum foil, and let rest for 5 to 10 minutes.
Meanwhile, pour off all but 2 teaspoons fat from now-empty skillet. Add shallot and cook over medium heat until softened, about 1 minute. Stir in ketchup and thyme and cook until fragrant, about 30 seconds. Add broth and wine and simmer, scraping up any browned bits, until reduced to 1/3 cup, about 10 minutes. Carve bone from steak and cut steak on bias into four 1/2-inch-thick slices. Serve with jus.