Slice the tenderloin into 8 pieces and pound till they're 1/4 inch thick.
Place the flour on a plate. In a shallow bowl, beat the eggs. Chop the parsley. In a separate bowl, combine the bread crumbs, parsley, 1 1/2 teaspoons of the salt, and 1/4 teaspoon of the pepper. Dip each cutlet in the flour, then in the beaten egg, and finally in the bread crumbs.
Heat 2 tablespoons of the oil in a large skillet over medium heat. Working in batches, cook the cutlets until golden and cooked through, 2 to 3 minutes per side, using 2 more tablespoons of the oil for the second batch.
Transfer to plates. Wipe out skillet.
Heat the remaining oil over medium-high heat.
Add the tomatoes to the skillet with the vinegar, thyme, and the remaining salt and pepper. Cook for 7 minutes. Before removing the tomatoes from the heat, add the spinach and capers and cook until the spinach wilts, about 1 minute. Divide the pork among individual plates and top with the spinach mixture.