Juicy Tomatoes With Parmesan-Olive Bread Crumbs

ripe, such as a mix of cherry, campari and heirloom varieties

day-old, without crust

thinly shaved or coarsely grated

such as Castelvetrano, picholine or Cerignola, roughly chopped

finely grated, or lemon, or a combination

or red-pepper flakes, or a combination

or white