1Preheat oven to 425F convection (or 450F regular bake).
2Make Caesar dressing: Whisk together egg yolk, lemon juice, and Dijon mustard. Slowly add avocado oil, whisking to incorporate. Mix in anchovies, garlic, and Parmesan. Adjust taste and refrigerate.
3Place a wire rack on a baking sheet, spray with oil.
4Pound chicken breasts to 1/4-inch thickness between plastic wrap. Season with salt and pepper.
5Coat chicken in flour, then egg, then breadcrumb mixture. Place on wire rack.
6Spray chicken with oil, convection bake for 12-15 minutes at 165F internal temperature. Option to broil for extra crispiness.
7Toss romaine and shaved Parmesan with half the Caesar dressing, add more if needed.
8Serve salad on top of chicken, garnish with Parmesan and lemon.