Trim any membrane and excess fat from the pork cheeks, then season all over with salt and pepper. Dredge lightly in flour, shaking off any excess.
Heat the olive oil in a large Dutch oven or heavy pot over medium-high heat. When hot, sear the cheeks on all sides until well browned and caramelized, about 4 to 5 minutes per side. Transfer to a plate and set aside.
Add the onion, carrots, and leek to the same pot. Cook over medium heat, stirring occasionally, until the vegetables are soft and lightly browned, about 10 to 15 minutes.
Stir in the garlic and cook for another 2 minutes, until fragrant.
Pour in the red wine and bring to a rolling boil. Boil for 2 to 3 minutes, scraping up any browned bits from the bottom of the pot.
Add the beef broth, bay leaves, and thyme. Return the pork cheeks to the pot, making sure they're submerged in the liquid.
If you're using a pressure cooker, cook on high pressure for 45 to 50 minutes, then allow the pressure to release naturally before opening. Otherwise, cover the pot and simmer gently over low heat for 2 1/2 to 3 hours, until the cheeks are fork-tender.
Transfer the cheeks to a plate and discard the bay leaves and thyme sprig. Use an immersion blender to puree the cooking liquid and vegetables in the pot until smooth. If the sauce is too thin, simmer uncovered for a few minutes to thicken. Taste and adjust the seasoning with salt and pepper.
Return the pork cheeks to the sauce to warm through. Serve hot with mashed potatoes, fries, or white rice.