Preheat the oven to 400°F (200°C) and lightly spray or oil a large baking sheet or casserole dish.
Pat the chicken breasts dry with paper towels. Slice each breast horizontally into two thin filets to make four pieces total, or use pre-sliced cutlets.
Crack the egg into a shallow bowl and whisk until well beaten.
On a large plate or shallow bowl, combine the breadcrumbs, parmesan (if using), gluten-free flour, garlic powder, 1/2 tsp sea salt, and black pepper; mix until evenly distributed.
Dip one chicken filet into the beaten egg, coating both sides, then press both sides into the breading mixture to fully coat. Place the breaded filet on the prepared baking sheet; repeat with remaining pieces.
Drizzle or brush the 1/3 cup oil evenly over the breaded chicken pieces to help them brown in the oven.
Bake on the center rack for 12 to 15 minutes, until golden and the internal temperature reaches 165°F (74°C). Use a meat thermometer inserted into the thickest part to check doneness.
While the chicken bakes, combine the Dijon mustard, cider vinegar, honey, and 1/4 tsp sea salt in a small bowl or blender and mix until smooth to make the honey-Dijon sauce.
Serve the baked breaded chicken hot with the honey-Dijon sauce as a drizzle or dipping sauce.