Wash and then cut potatoes into quarters, place them in a large microwave-safe bowl. Add enough water into the bowl so that it comes up 1 inch. Microwave for 5 min, or until potatoes are easily pierced with a fork. Add more water if needed.
While the potatoes are in the microwave, cut the broccoli into bite-size pieces and cut the ham into 1 x 1" cubes.
Drain excess water from the potatoes. Add broccoli, ham, olive oil, salt, Italian seasoning, pepper, and garlic to the potatoes. Mix
Take 12" piece of foil. Fold in half so that the two shorter sides meet. Make a half an inch fold on each side of the packet. Then fold again so that each side is folded twice. Stand up the foil packet and open it up, try to make the bottom flat. It should look like a pouch. Repeat 3 more times
Divided the mixture into the four pouches. Fold the top of the pouches.
Cook for 30 minutes, until broccoli and potatoes are tender.
Carefully open up and top with ¼ cup of cheese.
If there is excess water at the bottom of the pack, poke a hole in the bottom and let it drain.
Notes
At the deli counter I ask for the thickest slice of ham they can do, and let them know I will be cubing it.