Season the short ribs on all sides with salt and black pepper.
Heat the vegetable oil in a large skillet over medium-high heat. Brown the ribs in batches until they have a deep color on all sides, then set them aside.
Place the sliced onion and minced garlic in the bottom of the slow cooker. Arrange the browned ribs on top.
In a small bowl, stir together the brown sugar, bourbon, beef broth, and soy sauce until the sugar dissolves. Pour this mixture over the ribs.
Cover and cook on low for 8 hours, until the meat is very tender and pulls easily from the bone.
Remove the ribs to a serving platter. Spoon some of the sauce over the top and sprinkle with fresh parsley before serving.