Cook bacon in large skillet over medium heat until crisp, about 5 minutes. Transfer bacon to paper towels to drain.
Melt 1 tablespoon butter in medium nonstick skillet over medium-high heat. Add apple slices; saute 4 minutes. Remove from heat.
Spread mustard on cut sides of bread. Place 2 cheese slices on each bottom bread piece, top with 4 to 5 apple slices, then 3 bacon slices. Top each with 2 more cheese slices, then bread pieces. Press sandwiches lightly to compact.
Melt 1 tablespoon butter with 1 tablespoon oil in each of 2 large nonstick skillets over medium heat. Add 2 sandwiches to each skillet. Cover skillet; cook until bottoms of sandwiches are brown, pressing with spatula to compact, about 5 minutes. Turn sandwiches over; cover and cook until brown on bottom and cheese melts, about 5 minutes.
Note: Use a panini press for step 4 if you have one.