Heat the oven to 425°F and line a rimmed sheet pan with parchment.
Rub the chicken with 1 tablespoon Dijon, olive oil, salt and black pepper and place it on the prepared pan.
Roast for 16 to 19 minutes, until the thickest part of each cutlet reaches 165°F.
Top each cutlet with cheddar and roast for 1 minute more, just until the cheese softens.
Whisk the mayonnaise, maple syrup and remaining Dijon and toast the rolls in the oven for 2 minutes.
Spread each roll with maple-Dijon mayo and add 1 cheesy cutlet and 4 apple slices.