Place chicken breasts between two sheets of plastic wrap and pound to an even thickness.
In one shallow bowl, mix breadcrumbs, Parmesan, garlic powder, Italian seasoning, and salt. In another bowl, beat the eggs with a splash of water.
Dip each chicken breast in the egg, then coat with the breadcrumb mixture.
Heat a skillet over medium heat with a drizzle of olive oil. Sear the chicken cutlets on both sides until golden brown (about 3 minutes per side). Transfer to a baking sheet and bake for 10-12 minutes, until cooked through.
Prepare the dressing:
Blend the dressing ingredients in a blender or food processor until smooth and thickened. Taste and adjust seasoning as needed.
Assemble the salad:
In a large bowl, toss Romaine lettuce with the dressing. Top with shaved Parmesan.
Serve:
Place a chicken cutlet on each plate and top with a generous portion of Caesar salad. Garnish with additional Parmesan if desired.