The filling starts by cooking the beef, onions, and garlic in a large pot or skillet. This is accomplished using medium-high heat until the seasoned meat is no longer pink and onions are translucent. Paprika and thyme can be stirred in and cooked for 1 more minute. Add the peas, carrots and corn and mix the ingredients well.
Use either a medium bowl or measuring cup to whisk together the broth, flour, chili sauce and Worcestershire sauce. Then add these to meat and veggie mixture, adding some salt and pepper. Heat is then reduced to medium-low, letting it simmer for about 5 minutes. Expect the mixture to thicken slightly. Cover the dish and remove from heat while you prepare potato and squash topping.
The topping is made by placing the potatoes in a large pot and covered with water using salt if desired. Boil the water and then add the squash. Cook these until they are tender, about 12 to 14 minutes. Drain the water. Sprinkle ½ cup Parmesan over potatoes and squash. Cover the lid to allow the cheese to melt. After a minute, add the sour cream, salt and dash of nutmeg. Mash together well with potato masher. Minimize the lumps as best as possible.
To assemble casserole, the meat mixture is spread out evenly over the bottom of the casserole dish. The potato/squash mixture is then placed on top. Parmesean Cheese can be sprinkled on the top of potatoes. For 25 minutes, bake at 375ºF. This is done until its bubbly around the edges and completely heated through. Remove from oven and if desired sprinkle on top some fresh chopped parsley garnish. Let the casserole stand for 5 minutes before it is ready for serving.