Heat oil in a large skillet over medium-high heat.
Season the chuck with a generous amount of salt and pepper, then toss it in flour. Once the oil in the skillet is hot and shimmering, place the chuck into the skillet to give it a quick sear, about 2-3 minutes. Don't fully cook the beef. We just want a nice crust on the outside. When done, transfer the beef to the slow cooker; put the skillet back on the stove.
Pour 1 cup of beef broth and 1 cup of Guinness into the skillet. Bring to a simmer, and add the tomato paste. Deglaze the pan by scraping the bits left behind from the beef. Simmer for about 5 minutes, then transfer the liquid to the slow cooker.
Add the garlic, shallots, carrots, turnip, mushrooms, and thyme sprigs to the slow cooker. Give everything a good toss, then add the remainder of the beef broth and Guinness. Cover, and cook on low for 7-8 hours. If cooking on high, only cook for 3-4 hours.