Preheat the oven to 400°F (200°C). Spray a large baking sheet or casserole dish with cooking oil or line with parchment.
Prepare the chicken: pat 2 large chicken breasts dry with paper towels. Slice each breast horizontally to make four thin filets, or use thin cutlets/tenders if you have them.
Beat the egg in a shallow bowl with a fork until well combined.
On a large plate or shallow bowl, combine 2/3 cup breadcrumbs, 1/2 cup grated Parmesan (if using), 3 Tbsp flour, 1 tsp garlic powder, 1/2 tsp sea salt, and 1/4 tsp black pepper; mix until uniform.
Dip each chicken filet into the beaten egg, coating both sides, then press into the breading mixture to coat thoroughly. Press extra breading onto the chicken if you want a thicker crust. Transfer breaded filets to the prepared baking sheet.
Drizzle or brush the breaded chicken with 1/3 cup olive oil or avocado oil to help browning.
Bake on the center rack for 12 to 15 minutes, until golden and the internal temperature reaches 165°F (74°C). Use a digital thermometer inserted into the thickest part for an accurate reading.
While the chicken bakes, make the honey mustard sauce by whisking 3 Tbsp Dijon mustard, 2 Tbsp cider vinegar, 3 Tbsp honey, and 1/4 tsp sea salt together until combined. Adjust salt to taste.
Serve the baked breaded chicken hot with the honey mustard sauce on the side or drizzled over the chicken.