Blot roast dry with paper towels. Sprinkle roast with Cajun seasoning, salt, and pepper.
Heat oil in a large skillet over medium-high heat. Add pork and sear on all sides. Transfer to a 6-quart slow cooker.
Scatter the garlic on top of and around pork. Sprinkle the thyme and red pepper flakes over pork.Scatter butter over pork.
Place lid on slow cooker and cook on LOW for 5 to 7 hours or on HIGH for 4 to 5 hours.
Pour cooking juices into a medium saucepan. Place cornstarch in a small bowl and add 3 tablespoons of beef broth. Stir until mixed. Pour into saucepan along with remaining beef broth.
Bring to a simmer for 2 to 3 minutes to thicken. Season to taste with salt and pepper.