Preheat the oven to 450 degrees . In a small saucepan, heat 1 tablespoon olive oil over medium heat. Add the shallot and thyme and cook until softened, about 3 minutes. Add 2 cups blackberries, the wine, vinegar, honey and crushed red pepper; season with salt and black pepper. Bring to a boil, then lower the heat and simmer until the liquid is reduced by half, about 20 minutes.
Meanwhile, in a large, ovenproof skillet, heat the remaining 2 tablespoons olive oil over medium-high heat. Season the pork with salt and black pepper and cook, turning, until browned, about 10 minutes. Transfer the skillet to the oven and roast the pork until an instant-read thermometer registers 150 degrees , about 10 minutes. Transfer to a cutting board and let rest for 5 minutes before thickly slicing.
Strain the sauce through a fine-mesh sieve. Discard the solids, then return the sauce to the saucepan and season with salt and black pepper. Stir in the remaining berries and warm slightly over low heat. Divide the pork among plates and spoon some sauce over each portion.