Brush one side of each bread slice with oil; brush other side with mustard. Top mustard side of four slices with cheese, cucumber, spinach, and onion. Top with remaining bread slices, mustard side down.
Preheat indoor electric grill. Place sandwiches on grill. If using covered grill, close lid. Grill sandwiches until bread is golden. For covered grill, allow 3 to 5 minutes. For uncovered grill, allow 6 to 8 minutes, turning once halfway through grilling. Serve immediately. Makes 4 servings.