Trim any large sinew or fat from the beef cheek meat and season both sides with salt and black pepper
Heat olive oil in a large Dutch oven over medium-high heat and sear the beef cheeks on both sides until browned
Remove cheeks and set aside; add onion to the pot and cook until translucent, then add garlic and cook for 1 more minute
Stir in tomato paste and cook for 2 minutes to deepen flavor and deglaze the pan
Return the beef cheeks to the pot, add beef broth, rosemary, and thyme, and bring to a simmer
Cover with a tight lid and transfer to a preheated oven at 300°F (150°C); cook for 3 to 3.5 hours until fork tender
Remove beef cheeks and strain the braising liquid to make a rich sauce, reduce slightly if desired
Serve the beef cheek meat whole or shredded over creamy polenta, mashed potatoes, or buttered noodles