Add 1 tablespoon of olive oil to a large pan set over medium heat.
Season the beef with salt and pepper. Cooking in batches to allow a good sear, add the beef to the pan and allow to cook until browned, about 5 minutes per batch. Transfer the beef to a 6- or 8-quart capacity slow cooker.
Add the beef broth, tomato paste, Worcestershire sauce, balsamic vinegar, thyme, salt, and pepper to the slow cooker, stirring until mixed. Add the garlic, onion pieces, carrots, and cubed potatoes to the slow cooker.
Cover and cook on low for 7 to 8 hours or on high for 4 to 5 hours. I like cooking this dish slow and low so that the meat becomes tender and the flavors meld together.
Next, transfer 1 cup of the juices from the slow cooker to a medium-sized bowl. Whisk in the flour until there are no lumps.
Stir the flour mixture into the slow cooker.
Add the frozen peas and simmer, uncovered, on high for an additional 10 to 15 minutes, until the beef stew thickens slightly.
Serve immediately with French bread, cornbread, crackers, or biscuits that have been toasted.
