Step 1

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.

Step 2

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.

Step 3

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.

Step 4

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.

Step 5

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.

Step 6

Strain pork broth into a bowl.

Step 7

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.

Step 8

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.

Step 9

Spoon hot sauce over pork sections.