Trim the 650 grams beef cheeks of any excess fat and and then cut into 1.5-inch cubes. Season generously with salt and pepper.
Heat the 2 teaspoons vegetable oil in a dutch oven or other heavy bottomed pot over medium heat and then add the beef in a single layer. Brown on one side (4-5 minutes) and then flip and brown the other side. When the beef is browned, transfer to a bowl and set aside.
Turn down the heat and then add the 270 grams onion and 14 grams garlic to the pot. Cover and let the onions steam until tender (about 10 minutes). Remove the lid, add the 50 grams Anaheim peppers and then sauté until the onions are browned.
Add the 6 cups vegetable stock, 1 tablespoon paprika, 1 teaspoon caraway seed and 1 bay leaf, cover with a lid, and then let the beef cheek simmer over medium-low to low heat until it starts to get tender (about 45 minutes).
Drain and lightly rinse the 680 grams sauerkraut. When the beef is almost tender, add the 50 grams long-grain rice and sauerkraut to the Goulash. Cook until the sauerkraut and rice are tender (about another 30 minutes). Adjust salt to taste and serve with sour cream and dumplings, or boiled potatoes.