In a 5- to 6-quart slow cooker, place the beef, the contents of the spice packet (if included), carrots, and enought ale to cover the brisket.
Cook, covered, until the beef is tender, on high for 4 to 5 hours or on low for 7 to 8 hours.
Ten minutes before serving, thinly slice the Brussels sprouts. (This is easiest to do in a food processor with the slicing blade.).
Transfer the beef from the slow cooker to a cutting board; if the slow cooker is on the low setting, turn it to high. Add the Brussels sprouts to the carrots and liquid in the slow cooker. Cook, covered, until the Brussels sprouts are tender, 4 to 6 minutes.
Combine the sour cream, mustard, and tarragon.
Serve corned beef with the vegetables and sour cream sauce.