8 (1/2-inch-thick) slices sourdough bread (from a 9-inch round boule)
4 tablespoons unsalted butter, softened
4 teaspoons honey mustard
2 1/2 cups shredded, cooked chicken
1 1/2 cups grated cheddar cheese
1 small Gala apple, cored and cut into matchsticks
4 ounces Brussels sprouts (about 5), finely shredded with a knife or food processor attachment
1 tablespoon lemon juice
Freshly ground black pepper
Arrange a rack in the middle of the oven, place a baking sheet on the rack, and heat the oven to 450°F.
Spread the butter evenly on one side of each of the 8 slices of bread. Spread the honey mustard on the opposite side of 4 slices of the bread.
Using oven mitts, carefully remove the hot baking sheet from the oven. Place all the bread slices, butter-side down, on the baking sheet. Evenly distribute the shredded chicken among the mustard-spread bread slices, then distribute the cheese on the remaining 4 bread slices.
Return the baking sheet to the oven and bake until the cheese is melted and bubbling, about 10 minutes. Meanwhile, make the slaw.
Combine the apple, Brussels sprouts, and lemon juice in a small bowl. Taste and season with salt and pepper as needed.
Remove the baking sheet from the oven and transfer the bread slices with the chicken to a cutting board. Evenly distribute the apple and Brussel sprouts slaw over the chicken. Place the remaining bread slices cheese-side down on top of the slaw to close each sandwich. Cut each sandwich in half and serve.