Preheat an oven to 350ºF.
Sear the brisket. In a heavy bottomed dutch oven or braiser, heat oil over medium-high heat. Toss cubes of brisket with salt, pepper and paprika, and then the flour. Mix until evenly coated. Working in batches, sear the pieces of brisket until deep brown on all sides. Transfer to a plate.
Sauté the aromatics. Add the onions and leeks to the pot, adding a little more oil if necessary. Cook, stirring occasionally, until onions are soft and have picked up some of the brown bits on the bottom of the pot (from searing the beef).
Braise. Add beef back to the pot and nestle into the onions. Arrange cloves of garlic around the meat and evenly disperse carrots. Add beer and bring to a simmer. Simmer for 5- 10 minutes to temper some of the alchohol. Add the beef broth to the pot, cover with a lid and place in the oven for 2 1/2 hours.
Uncover. Uncover the pot and cook for another 45 min to 1 hour, until beef is tender and browned. If beef still isn't tender, cook for another 30 minutes. Remove from the oven, cover, and let the beef rest in the juices for 20 minutes.
Season before serving. Season the braising liquid with salt and pepper as needed before serving. Top with the minced chives. This brisket is great over creme fraiche mashed potatoes!