A precooked ham is gently re-smoked low and slow, then lacquered with a spicy apricot glaze and briefly caramelized for a glossy, sweet-savory crust and succulent slices.
Prepare grill for 2‑zone cooking and preheat to about 225°F (107°C) on the indirect side, or preheat smoker to 225°F (107°C).
Make 1 1/4 cups of Chris Lilly's Spicy Apricot Glaze; this can be done ahead.
Remove skin if present and trim fat to a very thin layer. Discard any prepackaged glaze and rinse off any glaze already on the meat. If spiral-sliced, run a little water into the slices to reduce moisture loss.
Place ham on the cooker (on a smoker, where it gets the most smoke; on a grill, indirect side flat-side down). Add 1–2 handfuls of wood for smoke. Close lid and smoke about 60 minutes.
Make a large double layer of foil (about 3 ft/1 m). Pour about 4 tablespoons glaze in the center, set ham flat-side on the glaze, then pour about half of the remaining glaze over the meat and brush to coat. Seal foil tightly.
Return ham to cooker. Insert a leave-in thermometer through the foil so the tip is about 1 inch (2.5 cm) from the bone and above liquid level. Maintain about 225°F (107°C) until internal temperature reaches about 130°F (54°C); then open foil, brush on more glaze, leave foil open to catch drips, and close lid. Note: reaching 130°F can take 3–4 hours depending on thickness and cooker accuracy.
After about 10 minutes, baste the ham with the pooled broth/glaze in the foil. Add more full-strength glaze if desired. Remove the foil and pour its juices into a saucepan; taste and adjust with more glaze or broth, then keep the sauce warm.
Move ham over direct heat (glaze facing the heat) and caramelize the surface, watching closely so it doesn’t burn, about 3–4 minutes per area; roll to sizzle and caramelize all sides except the flat side.
Remove from heat, slice, and serve with the warm pan sauce/glaze.