Preheat a grill to high. Puree the plum tomato, sun-dried tomatoes, vinegar, garlic, oregano, a few basil leaves and 2 tablespoons parmesan in a blender, drizzling in the sun-dried tomato oil until smooth. Add 2 to 3 tablespoons water, if needed; season with salt and pepper.
Halve the chicken breasts horizontally to make four 1/4-inch-thick cutlets. Brush with 1 tablespoon olive oil and season with salt and pepper. Grill the chicken until marked on the bottom, about 4 minutes, then turn and grill until cooked through, about 3 more minutes. Transfer to a cutting board.
Heat the remaining 2 tablespoons olive oil in a large skillet over medium-high heat. Add the breadcrumbs, season with salt and pepper and cook, stirring occasionally, until golden, about 2 minutes. Add the remaining 3 tablespoons plus 1 teaspoon parmesan and the parsley and cook until toasted, about 1 more minute.
Toss the salad greens and remaining basil in a large bowl. Cut the chicken into pieces and add to the greens along with the mozzarella. Toss with the dressing, then sprinkle with the breadcrumb mixture.
Photographs by Kate Sears
Courtesy of Food Network Magazine