Whisk together mayonnaise, olive oil, lemon juice, garlic, Worcestershire, and mustard until smooth.
Stir in grated parmesan and season with salt and pepper.
Refrigerate dressing until ready to use.
Preheat oven to 350F and line a baking sheet with parchment paper.
Toss sourdough cubes with olive oil, salt, and garlic powder.
Spread on baking sheet and bake for 15 minutes, tossing halfway through, until golden and crispy.
Pound each chicken breast between plastic wrap to 1/4-inch thickness.
Season both sides with salt and pepper.
Set up breading station with seasoned flour, beaten eggs, and breadcrumbs mixed with parmesan.
Dredge each chicken breast in flour, shaking off excess.
Dip in beaten eggs, letting excess drip off.
Press firmly into breadcrumb mixture, coating both sides well.
Heat 1 tablespoon butter and 1 tablespoon olive oil in a large skillet over medium-high heat.
Add 2-3 chicken breasts and sear for 4-5 minutes per side until golden brown and internal temperature reaches 165F.
Transfer to cooling rack and sprinkle with flaky sea salt.
Repeat with remaining chicken, adding more butter and oil as needed.
Toss chopped little gem lettuce with Caesar dressing until lightly coated.
Add croutons and grated parmesan, tossing gently.
Arrange salad on plates and top with sliced crispy chicken.
Garnish with shaved parmesan, cracked black pepper, and lemon wedges.