In a stockpot or Dutch oven, heat oil over medium-high heat; add brats and cook until browned on all sides. Remove from pan; set aside.
Add onions, apple and garlic to pan; salt and pepper to taste. Sauté until onions are caramelized (about 5-7 minutes). Stir in sauerkraut, beer or chicken broth, sugar and mustard; bring to a boil.
Reduce heat to simmer. Add brats to pan and cover; simmer 45 minutes, stirring occasionally. Remove brats from pan; strain sauerkraut. Serve brats on buns with kraut.