- Preheat oven to 400 degrees.
- Pat steaks dry with paper towels and season generously with the salt and pepper. Heat the oil and the butter in a large cast iron skillet over medium-high heat until very hot. Add the steaks to the pan and cook 2-3 per side. Turn and brown the sides of each steak. Place the pan in the oven and cook for an additional 2 minutes (to an internal temperature of 135 degrees). Let the steak rest for 8-10 minutes.
- Meanwhile in a medium saucepan heat the heavy cream over medium heat; cook for 15-20 minutes. Stir in the Pecorino Toscano and the Parmigiano-Reggiano; cook for an additional 5 minutes then stir in half the blue cheese and the rosemary. Season to taste with salt and pepper.
- Spread a tablespoon of the blue cheese sauce on each of 4 serving plates and top with a steak. Spoon additional sauce over each steak and mound potato sticks (recipe follows) to the side. Garnish each steak with the remaining blue cheese and fresh rosemary sprigs.
- For Potato Sticks: Pour oil about 3 inches deep in a deep, heavy skillet and heat over medium heat. Add Rosemary sprigs to the oil. When the oil is very hot add the potato sticks and cook in batches until golden brown and crisp.