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 to make four thin filets, or use pre-sliced cutlets; aim for about 1/2 inch thickness.
Beat the large egg in a shallow bowl until well combined.
On a separate 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 to combine.
Dip each chicken filet into the beaten egg to coat both sides, then press into the breading mixture to fully coat; repeat to create a thicker crust if desired. Place breaded filets on the prepared baking sheet.
Drizzle or brush the olive or avocado oil over the breaded chicken pieces to help them crisp while baking.
Bake on the center oven rack for 12 to 15 minutes, or until the crust is golden and an instant-read thermometer inserted into the thickest part reads 165°F (74°C).
While the chicken bakes, combine the Dijon mustard, cider vinegar, honey, and 1/4 tsp sea salt in a small blender or bowl and whisk until smooth to make the honey-Dijon sauce.
Remove the chicken from the oven and let rest for 2 minutes, then serve with the honey-Dijon sauce as a drizzle or dipping sauce.
