Heat oil in a large heavy-bottomed skillet, or an electric frying appliance, such as in my case. Brown half of the meat in the hot oil and set aside. Add remaining meat; add onion when meat is nearly browned. After the onion is tender, two minutes or so, add the garlic to the onion/meat mixture and saute for a couple of more minutes.
In a 3 1/2- to 5-quart slow cooker, combine the broth, undrained tomatoes, barley, wine (if using), dried dillweed (if using), salt, and black pepper. Add the meat mixture and stir.
Cover; cook on low-heat setting for 8 to 10 hours or on high-heat setting for 4 to 5 hours. Before serving, stir in the roasted peppers and fresh mint. If using fresh dill, stir that in as well.