Step 1

Preheat grill to medium (350°F to 400°F) Stir together Dijon mustard and 1/4 cup of the mayonnaise in a small bowl. Spread about 1/2 tablespoon mayonnaise mixture on 1 side of each bread slice. Layer each of 4 bread slices with 2 cheese slices, 2 to 3 tomato slices, 1/8 teaspoon salt, 1/8 teaspoon pepper, and 2 bacon slices. Cover with remaining 4 bread slices, mayonnaise mixture-side down.

Step 2

Spread top of each sandwich with 1/2 tablespoon mayonnaise. Place sandwiches, mayonnaise side down, on oiled grates; spread remaining mayonnaise over tops.

Step 3

Grill sandwiches, uncovered, until bread is toasted and has grill marks and cheese is melted, 3 to 4 minutes per side.