In a large pot, combine the salt and sugar with 1 L of the water. Bring to a boil over moderately high heat, and stir until dissolved.
Once dissolved, stir in the peppercorns, chilies and limes. Add the remaining 2 L of water and the ice and stir until the ice has melted and the brine is at room temperature.
Once cool, add the ham. Cover the pot with plastic wrap, put a lid on and place the pot in the refrigerator for 24 hours.
Rub
The next day (when you’re getting ready to eat), preheat oven to 450 F.
Mix together all of the rub ingredients. Set aside.
Salsa
Mix together all of the ingredients in a medium bowl and set aside.
Assembly
Remove the ham from the brine and rinse under cold water to remove the brine. Discard the brine. Pat the ham dry with paper towels.
Cover the ham in the rub and place on a roasting rack in a baking dish. Pour the 1 cup of chicken broth into the bottom of the dish. Roast at 450 F for 10 minutes.
Reduce heat to 275 F. Roast for an additional 1 hour 45 minutes- 2 hours, or until an instant read thermometer reads 160 F.
Remove from oven and allow to rest tented for 30 minutes.