Heat a large skillet over medium heat. Add the ground beef and cook until it's no longer pink, breaking it up as it cooks. Stir in the onion and garlic, then continue cooking for 3 to 5 minutes until softened. Drain off any excess grease.
Transfer the beef mixture to the slow cooker, then spread the frozen mixed vegetables evenly over the top.
In a bowl, whisk together the beef broth, tomato paste, Worcestershire sauce, brown gravy mix, Italian seasoning, salt, and pepper. Pour the gravy over the meat and vegetables.
Cover and cook on LOW for 6 to 8 hours.
During the last 2 hours of cooking, peel and chop the potatoes into large chunks. Boil them in a pan of salted water for 15 to 20 minutes, or until fork tender. Drain well, then mash with the butter until smooth.
Give the beef filling a gentle stir and spread it into an even layer. Spoon the mashed potatoes over the top and spread them right to the edges.
Replace the lid and cook for the remaining 1½ hours.
Finish with a little chopped parsley, a pinch of salt and pepper, then serve warm.