Preheat a grill to medium-high (if you are using a charcoal grill, coals are ready when you can hold your hand 5 inches above grill for just 3 to 4 seconds). Using your hands, remove about 1/2 cup bread from each side of the loaf. Brush hollowed-out sides of bread with oil.
Grill kielbasa, flipping once, until browned and heated through, 8 to 10 minutes. Grill bread, flipping once, until lightly marked by grill, about 3 minutes.
Transfer kielbasa and bread to a cutting board. Halve kielbasa crosswise. Spread hollowed-out sides of bread with mustard; top each with half of the sauerkraut and a halved kielbasa ring. Cut each into 4 wedges. Serve immediately.