In a snug-fitting oven-proof vessel, combine the pork, julienned onions, garlic, thyme sprigs and black peppercorns. The the smaller the vessel, the less oil it will take to cover the ingredients. Just don't cram the pork into a tiny jar. It does need some space, but not a McMansion. Cover the pork and other ingredients with oil or lard.
Place the pork into a heated 300? F oven and bake it for 3 hours. At the end of 3 hours, pierce the pork with a fork and twist gently. If it pulls apart a little and looks like it would shred easily, remove it from the oven. If it seems tough, put it back in and let it cook till tender. It can easily take up to 4 hours. Remove the pork from the oven and let it cool in the oil. This step can be done up to 3 days in advance and the pork can be held, covered, right in the cooking container in the fridge.
Once the pork has cooled enough to handle, remove it from the oil. Let it drain, then shred the pork using two forks. Take note: if you have refrigerated the pork, gently warm it so it shreds easily. Cold meat doesn't shred well. Place the shredded pork in a bowl.
Fish the onions and garlic from the oil. Mince both and add them to the pork along with 4 tablespoons of the cooking oil. Also add the minced parsley and thyme. Mix with your hands to combine everything. Season with salt and pepper. Mix again then taste. Adjust the seasoning. If the pork seems like it can use it, add more oil. Just be careful not to add too much, making the final dish greasy.
Place the potatoes into a large pot of cold salted water, and by salted I mean at least a tablespoon of kosher salt. Place the pot over medium-high heat and bring the water to a boil. Cook the potatoes till tender.
Dump the cooked potatoes into a strainer. Let them steam dry for a minute or two. Using a potato ricer, rice the potatoes back into the empty boiling pot. Add the cubed butter, a two-finger pinch of salt and pepper. Stir to combine and add the mustard along with the half and half. Stir again. Taste for seasoning and adjust accordingly. Add more cream or milk if the potatoes seem stiff. They should be nice and fluffy.
Spread the pork out over the bottom of a casserole. Top with the potatoes and using a spatula smooth out the potatoes. Score the top of the potatoes with a fork. This creates all kinds of crunchiness so it is more than for looks, it has a purpose.
Bake in a 400? F oven till the interior is hot and the top is crunchy and golden. Serve with sharp salad greens dressed in a balsamic vinaigrette.