Toast the bread well. Let it cool at least 10 minutes. Using a food processor, grind the bread into crumbs. Mix in a bowl along with the pilaf and eggs. Season with salt if you decide it needs some.
Heat a tablespoon of so of oil in a large skillet over medium flame. Form the rice mixture into seven patties using a 3-inch round cutter. Cook the patties until golden on both sides, about 10 minutes each side. Transfer to a serving dish.
Preheat oven to 350° F. Spread a small dollop of pesto on each pattie. Top with a slice of mozzarella, another dollop of pesto, followed by a slice of fresh tomato. Repeat: Pesto, mozzarella, pesto, tomato, pesto, mozzarella. Spread a final bit of pesto on the white mozzarella.
Bake 20 to 30 minutes, until the cheese melts nicely and the patties are heated through.