Step 1

Using a utility knife or a sharp knife, carefully score skin of ham at 3/4 inches-1 inch intervals in a crosshatch pattern, taking care to cut just through skin and fat, not into the meat.

Step 2

Whisk sage, 1/4 cup salt, orange zest, and red pepper flakes in a small bowl. Rub salt mixture all over ham. Transfer ham and any excess salt mixture to a jumbo (2-gallon) resealable plastic bag. Place ham in bag on a large rimmed baking sheet and chill, turning ham every day to ensure even curing, for 4 days.

Step 3

Remove ham from bag and pat dry with paper towels. Let ham stand at room temperature for 2 hours.

Step 4

Arrange a rack in lower third of oven and preheat to 500°. Place ham, shank bone up, on a rack in a roasting pan.

Step 5

Roast ham until skin turns deep golden brown and starts to puff, about 20 minutes. Reduce heat to 325°. Carefully add 1 cup water to pan (it may spatter) and roast, rotating pan once, for 1 hour.

Step 6

Add 2 cups water to pan. Scatter star anise around ham; continue to roast, rotating pan every 45 minutes and adding more water if needed to maintain 1/4 inches liquid in bottom of pan, until skin is deep golden brown and crisp and an instant-read thermometer inserted into the thickest part of ham registers 140°, 1 1/2-2 hours more. If skin does not crisp within last 30 minutes of cooking, increase heat to 450° and roast about 5 minutes longer (watch closely).

Step 7

Transfer ham to a carving board; let rest for at least 30 minutes or up to 1 1/2 hours (the ham's internal temperature will increase as it rests to about 150°). Pour juices from roasting pan through a fine-mesh sieve into a large measuring cup; set juices aside and discard solids in strainer.

Step 8

Set roasting pan over two burners; add rye. Cook over high heat, scraping up any browned bits from bottom of pan, until rye is reduced by half, about 1 minute. Pour rye through same sieve into the measuring cup with ham juices. Chill in freezer for 15 minutes (this will make skimming the fat from the surface much easier).

Step 9

Skim fat from surface of juices; discard. Transfer juices (you should have about 1 cup) to a medium saucepan. Add orange juice and broth or 1 cup water. Bring to a gentle boil over medium-high heat. Cook until reduced to 1 1/2 cups, about 20 minutes.

Step 10

Remove pan from heat; stir in butter. Season sauce with salt, if needed. Carve ham. Pass sauce alongside.