Season pork chops with salt and pepper. Heat 2 tsp. oil in a large nonstick skillet over medium-high heat. Add the pork and cook until browned and just cooked through, 2 to 3 minutes per side. Transfer to a plate. Add remaining 1 tsp. oil to the pan. Add shallot and thyme; cook, stirring, for 30 seconds. Add port wine and blackberry juice, broth and vinegar; bring to a boil, scraping up any browned bits. Cook, stirring occasionally, for 5 minutes to reduce sauce and intensify flavor. Mix cornstarch and water in a small bowl. Add to the sauce and stir until lightly thickened. Reduce heat to low. Add blackberries and butter. Simmer, stirring, just until the butter has melted. Return the pork chops and any accumulated juices to the pan; turn to coat with sauce. Serve immediately.
Ready in 30 minutes