Trim root ends, coarse tops, and outer layers from leeks; cut leeks in half lengthwise. Rinse under running water, flipping layers to flush out grit. Coarsely chop.
Pour oil into a 6- to 8-quart Dutch oven or ovenproof pan over medium-high heat. When hot, add leeks and garlic; stir often until leeks are limp, about 10 minutes.
Meanwhile, rinse lamb shanks and pat dry. Add lamb, 1 cup water, orange slices, port, Cointreau, 1/2 teaspoon salt, and 1/2 teaspoon pepper to pan. Cover and bring to a simmer.
Transfer pan to a 325° regular or convection oven and bake until lamb is very tender when pierced, 2 to 2 1/2 hours. Check occasionally; if pan gets too dry, add water, 1/4 cup at a time, as needed. Uncover and bake until meat is well browned, 10 to 20 minutes longer.
Serve from pan, or spoon into a wide, shallow bowl. Add more salt and pepper to taste.