Remove silvery membrane from surface of the tenderloin with a sharp knife. Reserve the trimmings. Trim off the small "head" pieces of the tenderloin where there is a natural separation; this is optional. Reserve.
Cut tenderloin in half crosswise to make 2 equal portions. Cut each half lengthwise in half to make 4 pieces. Transfer to a bowl; refrigerate while you start the sauce.
Chop the reserved trimmings very fine. Melt butter in a pot over medium-high heat until caramelized and nicely browned, 4 or 5 minutes. Stir in broth and gelatin. Stir in water. Cook and stir over medium or medium-low heat at a low simmer until liquid is reduced by half, about 1 1/2 hours. Add more water if it reduces too quickly.
Place pork sections between to pieces of plastic wrap. Pound to a thickness of about 1/4 to 1/8 inch thick. Remove top sheet of plastic wrap. Turn each piece over. Sprinkle generously with salt and pepper. Dust very lightly with about 2 teaspoons flour. Flip back over; sprinkle with black pepper only. Press 3 sage leaves onto surface of each piece of pork. Cover completely with prosciutto, cutting or tearing strips to fit. A bit of overlap is okay.
Place sheet of plastic wrap back over the pork and pound very lightly to make sure the prosciutto sticks to the pork. Transfer to a plate; cover with plastic wrap. Refrigerate until chilled, at least 30 minutes.
Strain pork broth into a bowl.
Place skillet over high heat; add olive oil. When olive oil is hot and shimmering, place pork pieces in the oil prosciutto side down. Cook about 3 minutes. Carefully turn pieces and cook another minute. Remove skillet from heat. Transfer pork to warm serving plates.
Blot excess oil from skillet with paper towels. Add wine and pork broth. Cook over high heat until mixture thickens and reduces by about half, 4 to 5 minutes.
You can use veal or chicken breasts instead of pork in this recipe.
For a slightly slightly sweet finishing sauce, you can substitute Marsala wine for the dry white wine.
If you don't want to mess around making the fake pork stock with the chopped up trimmings, you can still use the gelatin trick, and simply dissolve a teaspoon into a cup of chicken broth, and reduce it by half. However, the browned scraps do add extra meatiness, and this way you won't have to feel guilty about trimming off too much meat.