Remove the steaks from the refrigerator and let them sit at room temperature for about 30 minutes.

Preheat your skillet over medium-high heat. Add the olive oil and heat until shimmering.

Season both sides of the steaks generously with salt and pepper.

Carefully place the steaks in the hot skillet. Sear for about 4-5 minutes on one side without moving them.

Flip the steaks and add 2 tablespoons of butter, minced garlic, rosemary, and thyme to the skillet.

As the second side cooks for another 4-5 minutes, tilt the skillet slightly and use a spoon to baste the steaks with the melted herb butter.

Remove the steaks from the skillet and transfer them to a plate. Cover them loosely with aluminum foil to rest while you make the gravy.

In the same skillet, reduce the heat to medium and add the flour. Stir constantly for about 1 minute to create a roux.

Gradually whisk in the beef broth, soy sauce, Worcestershire sauce, and Dijon mustard. Continue to whisk until the gravy thickens and becomes smooth, about 3-5 minutes.

Taste and adjust seasoning with salt and pepper as needed.

Slice the steaks against the grain and serve with the savory brown gravy drizzled over the top.