Season the beef all over with 1 teaspoon salt and 3/4 teaspoon pepper. In a 5-to 6-quart crock pot, heat the butter over high heat until hot. Sear the beef in batches, turning once, until browned, 6 to 8 minutes total. Transfer the beef to a plate as cooked.
Stir the onion into the crock pot, scraping up any browned bits, and cook, stirring occasionally, until golden, about 6 minutes. Place the beef, along with any accumulated juices, back into the pot and stir in the carrots, potatoes, beer, and stock. Simmer the stew on 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.
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