Cut the jalapeno into 4-6 large pieces including the seeds. Omit the seeds if you avoid spicy foods.
Place the pork in a large pot, pressure cooker or crock pot. Add the garlic, jalapeno chunks, cumin and cover with broth. Add water until the pork is fully submerged.
Cut one lime in half and squeeze the juice into the pot, toss it in the pot. Slice the remaining lime into quarters to be used at the table.
For the stovepot:
Bring up to a boil. Reduce to a simmer for about 2 hours until the pork flakes off when you use a fork.
For a pressure cooker:
Tightly covered, bring up to pressure. Simmer under pressure for 30 minutes. Reduce the pressure, by running it under cold water. Check to see if the pork flakes with a fork. Return to pressure if necessary for about 5-10 minutes. Check and repeat until the pork is falling apart.
For a crockpot:
Set on high heat for 4-6 hours or low heat for 6-8 hours. The time variations depend on the quality of your crockpot as older models sometimes take longer. Please know that this is a forgiving dish and the pork will usually benefit from a longer simmer. After removing the pork hunk, pour the poaching liquid into a saucepan.
After the pork is simmered, in any of the above three methods and falling apart, remove it from the poaching liquid. Tongs or two large spoons work for this job. Set it in the fridge to cool slightly. Remove the peppers, lime halves, and any other large pieces with a slotted spoon. Turn the heat up to high. Toss in the onion slices. Boil rapidly until the sauce is reduced in half or is at least thickened.
When the pork is cool enough to handle, pull it apart into shreds. Your clean hands or a fork work well.
Stir the pork into the sauce. Once it is steaming again, reduce the heat to low and enjoy as soon you are ready.
The pork also works well placed in a crockpot or chaffing dish to stay warm during a party.