Pierce the potatoes in a few places with a fork; microwave until slightly softened, about 4 minutes, then halve lengthwise. When cool enough to handle, grate the cut sides on the large holes of a box grater into a large bowl.
Add the sauerkraut to the grated potatoes along with the herbs, eggs, three-quarters of the scallions, 1 teaspoon salt, and pepper to taste. Stir in 1 tablespoon flour, then form into four 1/2-inch-thick patties. Sprinkle the patties with the remaining 1 tablespoon flour.
Heat the olive oil in a medium skillet over medium heat. Pierce the bratwurst all over with a fork, add to the pan and cook, turning, until golden brown, 5 minutes per side. Meanwhile, heat 1/3 inch olive oil in a large skillet over medium heat. Add the potato patties and cook until golden, 6 minutes per side. Drain on paper towels.
Remove the bratwurst from the skillet and reduce the heat to medium low. Add 1/2 cup water and bring to a simmer, then add the mustard and sour cream and stir until hot. Cut the bratwurst into pieces and serve with the potato cakes, sauce and the remaining scallions.
Photograph by Christopher Testani
Recipe courtesy Food Network Magazine