4 boneless, skinless chicken thighs or breasts (about 1 1⁄2 pounds)
Salt and freshly ground black pepper to taste
All-purpose flour for dredging
3⁄4 cup fine dry plain breadcrumbs
2 large eggs
1 cup vegetable oil, or as needed
3 ripe plum tomatoes, cored and thinly sliced
6 ounces fresh mozzarella or Italian Fontina cheese, sliced thin
For the Sauce
1⁄4 cup extra-virgin olive oil, plus more for drizzling over the finished dish
6 cloves garlic, peeled
8 ripe tomatoes, or 12 ripe plum tomatoes, peeled, seeded, and chopped
1⁄4 cup shredded fresh basil leaves
 Cut off any fat, bone, and gristle remaining on the chicken thighs. Place two thighs between two sheets of plastic wrap. Pound them lightly with the toothed side of a meat mallet to a more or less even thickness.
 Season the chicken thighs lightly with salt and pepper. Spread out the flour and breadcrumbs on two separate plates. Beat the eggs in a wide, shallow bowl until thoroughly blended. Dredge the chicken in flour to coat lightly, and tap off excess flour. Dip the floured thighs in the beaten egg, and hold them over the bowl to let the excess egg drip back into the bowl. Transfer the chicken, one piece at a time, to the plate of breadcrumbs; turn it to coat with bread- crumbs, patting gently and making sure that each thigh is well coated.
 Heat the vegetable oil in a wide, heavy skillet over medium-high heat until a corner of one of the coated thighs gives off a lively sizzle when dipped in the oil. Add to the oil as many of the chicken pieces as fit without touching. Fry, turning once, until golden on both sides and cooked through, about 8 minutes. Remove to a baking sheet lined with paper towels, and drain well.
 Remove the paper towels from the baking sheet. Top each chicken thigh with overlapping slices of tomato, dividing the tomatoes evenly. Drape the sliced cheese over the tomatoes to cover the chicken completely.
 Preheat the oven to 400 degrees F.
 Prepare the sauce: Heat 3 tablespoons of the olive oil in a wide nonreactive skillet. Whack the garlic cloves with the side of a knife, and drop them into the oil. Cook, shaking the pan, until golden brown, about 2 minutes. Carefully slide the chopped tomatoes into the skillet, season lightly with salt and pepper, and cook until lightly thickened, about 10 minutes. Remove from the heat, an set aside.
 Bake the chicken until the cheese us lightly browned, about 10 minutes. While the chicken is baking, reheat the tomato sauce to keep it simmering, stir in the basil, and taste, seasoning with salt and pepper if necessary. Spoon the sauce onto a heated platter or plates, and place the baked chicken over the sauce. Drizzle the remming olive oil over the sauce, and serve immediately.