Place peeled and diced potatoes with 1 cup of chicken broth in the Instant Pot. Cook on high pressure for 8 minutes, then quick release. Add dairy-free milk, plant-based butter, and ½ tsp salt, then blend with an electric hand mixer until smooth and creamy. Adjust seasoning to taste.
Preheat to 400°F. Prepare a casserole dish with cooking spray.
In a large sauté pan, brown ground beef with onion and celery over medium-high heat, breaking it apart as it cooks. Drain excess fat. Add mushrooms, if using, and cook until tender.
Sprinkle gluten-free flour over the beef mixture, stirring to coat. Add beef broth, tomato paste, Worcestershire sauce, rosemary, thyme, garlic, parsley, salt, pepper and frozen vegetables. Simmer over low heat for 5-10 minutes until the mixture thickens.
Spread the meat mixture evenly in the casserole dish. Top with mashed potatoes, spreading evenly to cover. Sprinkle with paprika.
Bake for 20-25 minutes. Broil for 1-2 minutes for a golden potato topping.
Let cool for 5 minutes before serving. Enjoy this wholesome, comforting dish!