Cut the chuck into large pieces and season with salt and pepper.
In a large pan, heat 1 T olive oil over medium high heat. [Note: if you have a multi-cooker, you can do all the browning steps in your slow cooker on the saute setting and save yourself a dish.] Add the chuck roast pieces, working in batches if necessary, and brown on all sides. Remove and set aside.
Add the chopped onions and garlic, and saute until the juices from the meat have been absorbed and the onions have softened. Stir in the anchovy paste.
Add the beef and any accumulated juices to the insert of a crockpot. Add the sautéed onions and garlic, as well as the tomatoes, oregano, beef broth and wine.
Cook on LOW for 6 hours. Remove the beef and shred. Stir back into the sauce and skim off as much fat from the top as you can. Season to taste with salt and pepper.
Serve with your pasta of choice or polenta.