Use paper towels to pat dry the steaks and let rest at room temperature for 20 minutes.
Coat the steaks all over with 2 teaspoons salt and black pepper.
In a large skillet, heat olive oil and 1 tablespoon butter over medium-high heat. Add steaks and cook until a golden brown crust forms, about 4 minutes per side for medium rare. Transfer to a serving platter and tent loosely with foil.
Pour off fat from skillet and melt another tablespoon of butter over medium-low heat. Add shallots and cook, scraping up brown bits, until soft and translucent, 3- 5 minutes. Add red wine and simmer until reduced by half. Add broth and thyme and simmer until a few tablespoons remain, about 5 minutes. Fish out and discard thyme sprigs.
Whisk in the remaining 4 tablespoons butter a slice at a time, whisking until completely melted. Taste and adjust the seasonings. Drizzle the sauce over the steaks, and serve immediately with more sauce on the side.