Preheat oven to 325°F. Position rack in lower third of oven.

Place ham flat side down in a large shallow roasting pan and score a diamond pattern about 1/8 inch deep into any fat. Sprinkle all over with 2 tablespoons sage and season with pepper. Bake until internal temperature reaches 140°F, 15 to 18 minutes per pound total cooking time. After the first hour, baste with pan juices about every 15 minutes.

Remove ham from the oven, transfer to a cutting board, and let rest 15 to 30 minutes.

While ham is resting, increase oven to 400°F. Arrange prosciutto on a baking sheet and bake until crisped, about 10 minutes. Set aside to cool.

Also while ham is resting, drain roasting pan, discarding liquid. Place pan on stovetop over medium-high heat. Add broth and wine; bring to a boil, and cook, scraping up any browned bits in the pan, until liquid is reduced to 1 1/2 cups, about 4 minutes depending on the size of the pan. Reduce to a simmer and add butter and remaining 2 tablespoons sage, stirring until butter melts. Whisk in flour mixture and cook, whisking, until sauce thickens, 30 to 60 seconds. Remove from the heat. Season with salt and pepper.

Carve ham and arrange on plates or a platter. Crumble prosciutto on top. Serve sauce on the side.

Substitutions: You can use bone-in or boneless ham and substitute dried sage (about 1 1/2 tablespoons) instead of fresh.