Place the potatoes in a large saucepan. Add the 1⁄2 teaspoon of sea salt and enough cold water to cover the potatoes.
Bring to a boil, then reduce the heat to medium and simmer, lightly covered, for 15 to 20 minutes, or until the potatoes are fork-tender.
Drain the water from the potatoes.
Add the 2 Tbsp butter and mash with a potato masher. Add the milk to the potatoes and mash again to incorporate. Season with pepper to taste. Add additional milk if needed to achieve desired consistency.
Then, make the filling:
Preheat the oven to 350 degrees F.
Place the dried bread in enough water to cover it. Let it soak for 15 minutes or until soft. After 15 minutes, drain the bread cubes. Squeeze off excess water.
In a large skillet or deep sauté pan, heat t⅓ cup of butter over medium heat. Add the onion and celery. Cook and stir for 5 to 10 minutes, or until the vegetables are tender. Add the parsley and bread cubes and cook and stir for a few more minutes.
Add the bread mixture and the eggs to the mashed potatoes. Stir to combine.
Place in a lightly oiled 2.5-quart glass or ceramic casserole dish. Dot with a little butter. Cover and bake for 50 to 60 minutes, until the filling has puffed up and browned a little on top. You can uncover it during the last 10 or 15 minutes to brown the top.
Serve hot, garnished with fresh chopped parsley and gravy.