How to Make It
In a medium skillet, melt the butter with the caraway seeds and cook over moderate heat until fragrant, about 30 seconds. Add the sauerkraut and cook, stirring, until very dry, about 4 minutes. Transfer to a large bowl, add the 1/4 cup of dill and let cool.
Meanwhile, bring a large pot of salted water to a boil. Add the shredded potatoes and cook for 1 minute. Drain well, shaking out the excess water. Add the potatoes to the sauerkraut and stir to combine. Season with salt and pepper and let cool.
Heat a large griddle or cast-iron skillet over moderate heat. Brush with schmaltz. Working in batches, spoon 2-tablespoon-size mounds of the potato mixture onto the griddle and flatten into 2-inch rounds, about 1/2 inch thick. Cook, turning once, until the cakes are golden and crispy, 6 to 7 minutes; add more schmaltz to the griddle as needed. Reduce the heat to moderately low after the first batch and wipe the griddle occasionally.
Arrange the potato cakes on a platter and top with the crème fraîche, smoked trout, lemon zest and dill. Serve.