Pat the short ribs dry with paper towels and season all over with salt and pepper.
Place the seasoned short ribs in the basin of a 6-quart or larger slow cooker.
In a small bowl, whisk together the olive oil, minced garlic, red wine, beef broth, and Worcestershire sauce.
Pour the liquid mixture over the short ribs in the slow cooker.
Cover and cook on LOW for 8 hours or on HIGH for 4-5 hours, until the meat is very tender and pulling away from the bone.
Carefully transfer the cooked short ribs to a platter and cover with foil to keep warm. Pour the cooking liquid through a fine-mesh strainer into a small saucepan.
Add the brown sugar to the saucepan with the strained liquid. Bring the mixture to a boil over medium-high heat, stirring constantly until the sugar dissolves.
Reduce the heat to maintain a steady simmer and cook for 3-5 minutes, stirring occasionally, until the sauce has thickened into a glaze that coats the back of a spoon.
Serve the warm short ribs with the hot glaze spooned over the top.