Place the thick onion wedges into the bottom of a 6-quart slow cooker and drizzle with olive oil.
Layer the sliced sausage pieces on top of the onions.
In a small bowl, whisk together the balsamic vinegar, brown sugar, Dijon mustard, garlic, thyme, and pepper.
Pour the balsamic mixture over the sausages and onions.
Cover and cook on the LOW setting for 4 to 5 hours (or HIGH for 2 hours) until the onions are tender and caramelized.
Stir the mixture gently halfway through to ensure everything is evenly coated in the glaze.
Serve the sausages and onions warm directly from the pot or on a platter with toothpicks.
Garnish with fresh chopped parsley before serving.