Place a rack in the center or upper third of the oven and preheat to 425 degrees.
Slice the pork loin crosswise into 6 equal pieces. Trim fat if there’s a lot but leave a thin layer, for moisture and flavor. [Nick the fat and skin around each cutlet so it won’t twist and tighten the meat during cooking.] .Pound each piece with a mallet (or the flat bottom of a heavy pan) to tenderize and flatten to 1/2-inch thickness.
Rinse and dry the tomato (or tomatoes). Cut out the core neatly and slice off this top 1/2 inch of the tomato, where the core was, and about 1/2-inch of the curving bottom. Cut these pieces into 1/2-inch chunks for the pan sauce.
Now slice the center of the tomato into 1/2-inch thick rounds. Repeat with the second tomato if necessary so you have one beautiful round to top each cutlet.
Starting on the Stovetop
Put the olive oil and 1 tablespoon of the butter into the skillet, and set over low-medium heat. Strew the sage leaves around the pan and cook them slowly for a minute or two as the butter melts and starts to sizzle.
Salt the pork pieces, dredge them in the flour, and, when arrange all six in the pan. Cook at for about two minutes, then turn them over and let them brown slowly while you make the gratinate and the sauce as follows:
Pick out the cooked sage leaves and lay two on each cutlet.
Season each with pinches of salt and grinds of fresh pepper.
Place a thick tomato round on each cutlet and sprinkle with salt.
Raise the heat, and drop in the remaining butter, in pieces.
Spread the small chunks of tomatoes (and juices) in hot spots and let them start to cook for a minute.
Pour in the 1/2 cup of wine and 1/2 cup of Simple Vegetable Broth; shake the pan and raise the heat. Add more wine or Water if the sauce level is too low.
Finally, sprinkle 2 tablespoons or so of grated cheese on each cutlet.