Put oven rack in middle position and preheat oven to 325°F. Oil a large roasting pan.
If ham comes wrapped in plastic, rinse ham and pat dry. Cut away and discard any thick skin with a sharp paring knife, leaving a 1-inch band around shank end, then cut away all but about an 1/8-inch layer of fat where possible. Put ham, cut side down, in roasting pan. Pour 3/4 cup pineapple juice around ham and cover pan tightly with foil, then bake 1 hour.
While ham is baking, combine sugar and remaining 2 1/4 cups pineapple juice in a 1 1/2- to 2-quart heavy saucepan and gently boil, stirring occasionally, until reduced to 3/4 cup, 12 to 15 minutes. Transfer pineapple syrup to a bowl and cool 5 minutes. Whisk in mustard, salt, and pepper, then pour 1/2 cup into a small bowl and stir in thyme. Reserve remaining mustard mixture for serving.
Discard foil from pan and brush ham with thyme mustard mixture, then bake, basting with pan juices occasionally, until thermometer inserted into center of meat (do not touch bone) registers 145 to 150°F, 1 1/4 to 1 1/2 hours. If pan juices evaporate during baking, add 1/2 cup water. Transfer ham to a platter, discarding pan juices, and let stand, uncovered, 15 to 30 minutes before slicing. Serve ham with reserved mustard mixture on the side.
Cooks' notes: ·Pineapple mustard mixture, without thyme, can be made 1 day ahead and chilled, covered. ·Ham can be trimmed of skin and fat 8 hours ahead and chilled, its surface covered with plastic wrap. Let stand at room temperature 30 minutes before baking.