Cut chicken breasts in half horizontally so you end up with 4 thin pieces of chicken.
Working with 1 piece of chicken at a time, pound chicken until 1/4-inch thick. Set aside and repeat with the remaining 3 pieces.
Season with 3/4 teaspoon salt and black pepper, to taste.
Combine breadcrumbs and Parmesan cheese in a medium bowl. In another bowl beat eggs.
Dip cutlets in egg, then breadcrumbs.
Heat a large nonstick skillet over medium heat. If cooking in two batches, add half of the butter and olive oil.
When butter melts, add the cutlets and cook about 4 to 6 minutes on each side, until golden brown and cooked through. Repeat.
Slice the chicken cutlets. Arrange the baby greens in the center of the platter. Place the chicken, tomatoes, mozzarella, basil all round.
If making ahead, cover tight with plastic and keep chilled until ready to eat.
Or plate them individually if not making a platter, 1 piece chicken, 2 oz cheese and divide the salad.
Serve with 1 tablespoon vinaigrette (not included in n.i.).