Combine mayonnaise and mustard in a medium bowl. Add cheese and pepper, stirring well to combine (mixture will be very thick). Spread one-fourth of cheese mixture (about 2 tablespoons) over each of 4 bread slices. Top with remaining 4 bread slices.
Heat a large skillet over medium heat. Add 1 teaspoon oil to pan; swirl to coat. Place sandwiches in pan; cook 3 minutes or until lightly browned (do not flip). Remove sandwiches from pan. Add remaining 1 teaspoon oil to pan; swirl to coat. Turn sandwiches over, and add to pan; cook 3 minutes or until lightly browned and cheese melts. Serve immediately.