Preheat oven to 400ºF. Spread cornbread in a single layer on a rimmed baking sheet. Toast in the oven for about eight minutes or until dry and lightly golden, tossing once halfway through. Set aside to cool.
Meanwhile, whisk the vinegars, garlic, and olive oil together in a small bowl, seasoning to taste with salt and pepper.
Combine the tomatoes, vegetables, and mozzarella in a large serving bowl. (The recipe up to this point can be made a few hours in advance, then covered and refrigerated.) When ready to serve, fold the toasted cornbread and fresh herbs into vegetable and cheese mixture. Toss all ingredients with the vinegar dressing just before serving.