Season meat with 1 tbsp plus 1 tsp salt. Place vegetables, garlic, peppercorns, 1 tbsp salt, and tomato paste on the bottom of a large ovenproof pot with a tight-fitting lid (Dutch oven or stockpot) with pork on top. Cover with water three quarters of the way up, place the lid on the pot, and bring liquid to a boil on the stove top (should take about 15 minutes). Immediately transfer to the oven, letting roast braise until it is tender and falling apart, 2 to 2 ½ hours.
While pork is cooking, make potato topping. Peel potatoes and cut into large chunks (about 2 inches). Place in large pot, cover with cold water, bring to boil, and adjust heat to keep the water boiling without overflowing until potatoes are fork-tender, about 10 minutes. While potatoes are still hot, drain the water and add 2 tsp salt, butter (piece by piece), and cream (slowly), mashing potatoes with an old-fashioned beater or a manual potato masher as you go. The texture should be as silky as possible. Taste, season if necessary, cover, and let rest in a warm spot near the oven.
Remove pork from oven and let rest in liquid for about 20 to 25 minutes to ensure it will not get dry. Remove pork and reserve braising liquid. Carefully remove vegetables with a slotted spoon and transfer to an extra-large mixing bowl. Add thawed frozen peas. When roast is cool enough to handle, dice it into medium-sized chunks or just tear with a fork into shreds. Combine with vegetables and add enough cooking liquid to moisten meat mix without letting it get "stewy" (about ¼ to ½ cup), tasting and re-seasoning with salt and pepper if necessary.
To assemble: First, potatoes must be hot in order to be spreadable. You can use any number or shape of baking pans or ovenproof casseroles you might have handy, with this guideline: The size of the pan must allow for about two inches of filling, which is then covered by potatoes.
Transfer meat mixture into the pans and carefully spread potatoes over the top, completely covering meat. Slide under the broiler to lightly crisp the top. Watch carefully — this will take only about 60 seconds.
To reheat: Bring dish to room temperature and place in preheated 325 degree oven until hot.