On a large plate mix together flour, salt, and pepper. Dredge the chuck roast on both sides.
Heat olive oil, on medium high, in a large pan. Place chuck roast in the pan and brown on both sides. This takes about 3-4 minutes on each side. Transfer beef to slow cooker.
In the same pan sauté garlic and shallots until fragrant and shallots are translucent, about 3-4 minutes. Stir in beef broth and scrap up any brown bits left from the roast. Transfer to the slow cooker with the beef.
In a bowl, whisk together balsamic vinegar, Worcestershire sauce, and brown sugar. Pour over the roast. Flip the roast a couple times to make sure the beef, balsamic mixture, shallots, and garlic are all combined. Cook on high for 5 hours or low for 8-10. Mine cooked perfectly on high for 5 hours.
Removed roast from slow cooker and place in bowl or on a plate. Shred the meat. It should fall apart. Pour some of the leftover sauce onto the shredded beef. Add ¼ teaspoon of salt. Mix well and serve.
Make ahead tips This recipe can be cooked completely ahead of time and frozen into portions for future lunches or dinners. Heat up on the stove or in the microwave when ready to eat.