Season the brisket all over with 1 1/2 teaspoons salt and 3/4 teaspoon pepper. In a 5-to 6-quart crock pot, heat the oil over high heat until hot. Sear the brisket, turning once, until browned, 6 to 8 minutes total. Transfer the brisket to a plate.
Stir the onion, mushrooms, and garlic into the crock pot, scraping up any browned bits, and cook, stirring occasionally, until golden, about 6 minutes. Place the brisket, along with any accumulated juices, back into the pot and stir in the carrots, parsnips, rutabaga, beer, Worcestershire, and stock. Simmer the brisket over low, covered, until the meat is very tender, about 6 hours. Increase the heat to high. Stir the flour together with 2 tablespoons cold water, then whisk into the simmering liquid. Simmer the brisket, uncovered, until the liquid is slightly thickened, about 10 minutes. Season with salt and pepper to taste, then serve, sprinkled with the dill.
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