1. Whisk milk and potato flakes in large bowl. Add beef, 1/2 teaspoon salt, and 1/2 teaspoon pepper and knead until combined. Shape into four 1/2 inch thick oval patties and transfer to parchment lined plate. Refrigerate for 30 minutes or up to 4 hours.
2. Melt 1 tablespoon better in large nonstick skillet over medium-high heat. Cook patties unil well browned, about 5 minutes per side. Transfer to plate.
3. Add onion and remaining butter to empty skillet and cook until onion is softened, about 5 minutes. Add mushrooms and 1/2 teaspoon salt and cook until liquid has evaporated, 5 to 7 minutes. Stir in tomato paste and flour and cook until browned, about 2 minutes. Slowly stir in broth and port and bring to simmer. Return patties to skillet, cover, and simmer over medium-low heat until cooked through, 12 to 15 minutes. Season sauce with salt and pepper. Serve.