Peel the carrots and cut them into 1/2-inch dice. Peel the onions and cut each onion into four wedges. Set aside. Alternatively, use 2 cups of frozen pearl onions, thawed.

Heat the olive oil in a large skillet over medium-high heat. When the oil is hot and shimmering, add the lamb shanks. Cook the shanks turning frequently, until browned on all sides. Place the browned lamb shanks in the slow cooker.

Add the carrots and onion wedges to the lamb.

In a bowl, combine the wine with the mustard, vinegar, salt, pepper, rosemary, parsley, and garlic; set aside.

Add the mushrooms to the hot skillet used for the lamb. Cook the mushrooms about 5 minutes, stirring constantly. Spoon the mushrooms over the lamb shanks.

Pour the wine mixture into the skillet while stirring and scraping up the browned bits. Bring to a simmer; pour over the lamb shanks in the slow cooker.

Cover and cook on high for 2 hours. Reduce heat to low and continue to cook for 5 to 7 hours longer, or until the lamb shanks are very tender.

*If you don't have balsamic vinegar, substitute with 1 teaspoon of red wine or cider vinegar and 1/4 teaspoon of sugar.