Season beef, both sides, with salt and pepper. Place flour on a plate and dredge meat, both sides, in flour.
Heat 2 tablespoons of butter or drippings in a heavy Dutch oven over medium-high heat. Add beef and sear, turning, turning once, until browned, about 8 minutes. Transfer to a plate; set aside.
Add remaining butter or drippings, onions, and the teaspoon of brown sugar. Cover, cook 30 minutes, over very low heat, stirring after15 minutes. Remove lid; at this point, the onions should be very soft and starting to brown. Continue to cook, lid off, stirring every few minutes until caramelized and brown. Add a little water, a couple of tablespoons, if at any point it looks as if the onions are too dry and in danger of burning.
While onions cook, preheat oven to 325 degrees.
Add half the beer to the onions and continue to cook, scraping the bottom of the pan, until slightly reduced about three to four minutes.
Return beef to pot with remaining beer, vinegar, thyme, tarragon, bay leaf, mustard and salt, and pepper. Add beef stock as needed to bring the level of liquid 3/4’s of the way up the roast. Bring to a boil. Cover pot and place in oven until very tender (nearly falling apart) when pierced with a fork, three to three and a half hours.
Watch your liquid level and check now and then towards the end of the time, as timing and evaporation can vary with different ovens, pans, and thicknesses of roast. Add water if needed.
Place pot roast on a platter to rest for 10 minutes, stir jelly into the sauce. Taste and adjust seasoning and serve sauce with the roast.
Keywords: Alcohol, Bacon, Bargain Meal of the Week, Beef, Beef Stock, Beer, Caramelized Onion, Chuck Roast, Family Recipe, Freezes Well, planned leftovers, Pot Roast, Special Occasion