Season the Steaks: Pat ribeye steaks dry with paper towels, then generously season all sides with kosher salt and black pepper. Let the steaks sit at room temperature for 20–30 minutes if time allows.
Sear the Steaks: Heat oil in a large cast iron skillet over medium-high heat. Once hot, add steaks and sear for 4–5 minutes per side until deeply golden and cooked to your desired doneness. During the last minute, add 1 tablespoon butter and spoon the melted butter over the steaks. Remove steaks from the pan and let rest.
Start the Pan Sauce: Reserve 1 tablespoon of the steak drippings in the cast iron skillet and heat over medium. Once warm, add the minced garlic and shallots and sauté, stirring frequently, for about 1 minute until fragrant.
Deglaze and Reduce: Add the red wine, balsamic vinegar, rosemary sprig, and thyme sprigs to the skillet and bring to a rapid simmer over high heat. Let the mixture reduce until thickened to about ¼ cup, about 3–5 minutes.
Finish the Sauce: Add the beef stock and continue simmering over high heat until the sauce reduces and thickens to about ½ cup, about 4–5 minutes. Remove and discard the rosemary and thyme, turn off the heat, and whisk in the remaining 1 tablespoon of butter. Taste and season with additional salt and pepper as needed.
Serve: Spoon the red wine sauce over rested ribeye steaks and finish with chopped parsley and additional fresh herbs for garnish. Serve immediately.