Fill an 8 quart pot ⅔ of the way up with cold water and salt generously. Peel the potatoes, cut into 1-2 inch cubes, and transfer to the pot.
Bring the pot with the potatoes to a boil over high heat and boil for 10 minutes. The potatoes should be tender enough to be easily pierced with a fork, but should not be so soft that they completely fall apart when pierced.
Drain the potatoes in a colander, and leave the pot off the heat nearby. While the potatoes are still hot, press the potato pieces through a potato ricer back into the 8 quart pot. When all of the potatoes have been riced, add the milk or buttermilk, 3 tablespoons of the butter, and 1/2 teaspoon of salt to the pot and gently fold until just combined. Set aside.
In a medium bowl, combine the ground beef or lamb with the baking soda and 1 teaspoon of salt. Mix well with hands and set aside.
Heat the oven to 425F.
In a large saute pan, saute the onion with 1 tablespoon of the butter, the olive oil, and a pinch of salt over medium heat. Cook until softened, stirring occasionally, about 4 minutes.
Push the onions to the sides and add the ground beef or lamb to the pan. Push the meat out onto the pan and allow 2 minutes to brown undisturbed. Then continue to brown, breaking up with a wooden spatula or spoon and stirring occasionally, about 8 minutes more. If the mix becomes watery, turn the heat up a little to evaporate the liquid quicker.
Add the garlic, porcini powder, flour, a few cracks black pepper, and tomato paste, and cook 1-2 minutes, stirring. Add the stock and bring to a boil. Cook, stirring, until thickened, about 5 minutes.
Transfer the mixture to croques or a baking dish. Top with the frozen peas, followed by the mashed potatoes. Melt the remaining 1 tablespoon butter and brush on the top of the potatoes.
Bake for 30 minutes on the center rack, then broil on the center rack for 3-4 minutes. Serve topped with chives.