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Trim excess fat from brisket. Sprinkle salt and pepper on brisket.
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Heat oil in a large Dutch oven (about 7-quart) over medium-high heat until almost smoking.
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Add brisket to the pan and sear to brown on both sides, about 3 minutes per side.
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Add onions, water, and bay leaf. Cover and simmer for 1 1/2 hours.
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Drain sauerkraut and add it to the brisket. Add potato, apple, and caraway seeds.
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Toss to combine onions, sauerkraut, potato, apple, and caraway seeds.
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Bring to a boil then reduce heat to low. Cover and simmer for 30 minutes. Discard bay leaf.
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Transfer brisket to a cutting board. Allow to rest for 10 to 15 minutes. Thinly slice brisket across the grain.
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Serve brisket with sauerkraut.