Preheat oven to 325ºF. Let the chuck roast come to room temperature about a half hour before you're ready to cook. Pat the roast dry with paper towels and season with salt and pepper on both sides. Heat 2 tablespoons of olive oil in a large, lidded ovenproof skillet over medium-high flame. Brown roast on both sides, about 4 to 5 minutes per side. Reduce heat to medium when you turn the roast. Transfer roast to a plate.
Add onion to the pan, drizzling in more oil, if needed. Sweat the onion until in softens slightly and turns translucent, about 4 minutes, stirring frequently to avoid browning. Add garlic, juniper berries and tarragon to pan and cook, stirring, until fragrant, about 45 seconds. Add beer and broth to pan and bring to a boil, scraping up any browned bits. Season lightly with salt and generously with pepper. Return roast to pan along with any accumulated juices. Add bay leaves. Pour about 1 cup of water around roast—liquid should come about halfway up the sides of the roast—and bring to a boil. Cover pan and transfer to oven.
Cook roast for about 1 hour. Check to see that the liquids haven't cooked down too much. Add a little water, if needed. Turn the roast and cook for another 1/2 hour. Add carrots and potatoes, distributing around the roast and stirring to coat them with cooking liquids. Again, add a little water, if necessary (my pan's lid didn't seem to fit very tightly, and I got a fair amount of evaporation and cooking down). Vegetables do not need to be submerged in liquid.
Cook for another 1-1/2 hours, turning the roast and stirring the vegetables midway through. Roast and vegetables should be very tender at this point. Remove pan from oven. Transfer roast to a cutting board and tent with foil. Discard bay leaves, taste vegetables and sauce and adjust seasonings. Slice roast across the grain into 1/2-inch slabs. Arrange slices on individual plates, spoon potato carrot mixture alongside and spoon pan juices over everything. Serve.