Pat the round steak dry with paper towels. Season both sides generously with salt and pepper. Dredge in about 1/4 cup of flour, shaking off the excess.

In a large skillet or Dutch oven over medium-high heat, warm 2 tablespoons oil. When it’s shimmering, add the steak. Sear until nicely browned, about 3–4 minutes per side. Transfer steak to a plate and tent with foil.

Add the remaining tablespoon of oil and the butter to the pan. Lower heat to medium. Add the sliced onions and a pinch of salt. Stir occasionally, letting them soften and turn golden, 12–18 minutes.

When onions are soft, add the garlic and cook 30–60 seconds until fragrant. Sprinkle the remaining 1/4 cup flour over the onions and stir to coat.

Pour in the red wine (if using) and scrape up any browned bits. Add the beef broth, Worcestershire sauce, Dijon, and thyme. Stir until smooth and starting to thicken.

Return the steak to the skillet, nestling it into the gravy. Lower heat to a gentle simmer, cover, and cook for 45–60 minutes, or until fork-tender.

Remove the steak and let it rest a few minutes. If the gravy needs thickening, simmer uncovered or whisk in a slurry of cornstarch mixed with cold water. Slice and serve with gravy.