Heat the oil in a large skillet over medium-high heat until the oil begins to ripple.
Season the pork with salt and pepper, add it to the skillet, and sear until brown, about 6-8 minutes. Flip the loin and brown the other side, 6-8 minutes. Turn off the heat and transfer the pork to a large deep casserole or a small roasting pan.
Drain half the fat from the skillet. Set the heat to medium and sauté the onions for 2-3 minutes. Add the beer or chicken stock and stir with a wooden or heat-resistant spatula, being sure to scrape the bottom of the pan. Add the sauerkraut, stir, and transfer to casserole with pork loin. Cover and bake for 4-5 hours, or until the loin is fork-tender and pulls apart easily.
Meanwhile, prepare the dumplings. Combine the milk, beer, black pepper, and salt in a medium-size saucepan. Bring the mixture to a boil and whisk in the potato flakes. Reduce the heat to medium and continue to cook for 2-3 minutes, or until the mixture resembles mashed potatoes. Remove from heat and spread the mixture out onto a baking sheet. Set aside until completely cool.
Fit a stand mixer with a paddle attachment and combine the chives, baking mix, flour, nutmeg, eggs, and potato mixture in the mixing bowl until the dough begins to come together. Transfer the dough to a floured surface and continue to knead by hand until the ingredients are completely combined.
Roll the dough into a large square until it's about 1/4'' thick. Using a knife, pizza, or pastry cutter, cut the sheet of dough into 1'' x 1'' squares.
Bring the chicken broth to a boil in a 6-8 quart stockpot. Add 12-14 of the dumplings and return the broth to a simmer; cook 3-5 minutes. When the dumplings are floating and no longer sticky in the middle, remove the dumplings from the broth with a slotted spoon and place into a serving dish. Drizzle with oil to keep them from sticking together. Cover and keep warm until all the dumplings are cooked. Serve with pork and sauerkraut.
QVC is not responsible for the availability, content, security, policies, or practices of the above referenced third-party linked sites, nor liable for statements, claims, opinions, or representations contained therein. QVC's Privacy Statement does not apply to these third-party web sites.