Heat vegetable oil and butter in a large skillet over medium heat. Add onions and sauté for 5 minutes, or until onions are translucent. Add garlic and cook for 1-2 minutes, or until fragrant.
Add sprouts and cabbage to the onion mixture. Season with salt and pepper.
Brown vegetables for 5 minutes, stirring frequently.
Add mashed potatoes to the skillet, pressing down to flatten to form a patty. Brown about 6-7 minutes.
Carefully flip the potato and vegetable patty. Cook an additional 6-7 minutes, or until well-browned with a crispy crust. (If needed, invert potato onto a plate and slide back into skillet.)
Transfer onto a platter. Cut into wedges for serving.