Preheat the oven to 400 degrees F. 

Peel the parsnips, carrots, and potato (or potatoes) and cut them into 1/2-inch dice. Place them in a medium saucepan and cover with cold water. Set over high heat, cover and bring to a boil. Once boiling, remove the lid, decrease the heat to maintain a simmer, and cook until tender (approximately 15 minutes).

When they're done, drain in a colander and then return to the saucepan or pour into a large bowl. Roughly mash and then add the butter (or olive oil instead), milk, and goat cheese, and mash until smooth. I used an immersion blender to make it good and creamy. Add salt and pepper to taste.

While the potatoes are cooking, prepare the filling. Cut up the brussels sprouts, parsnip, carrots, and dice the onion. In a large saute pan or dutch oven, pour the oil and set over medium-high heat. Once the oil gets hot enough to shimmer, add the brussels sprouts, carrots and onion. Sauté just until they begin to take on color, about 3 to 4 minutes. Add the garlic and stir in.

Then add the ground meat, salt, and pepper and cook until browned and cooked through (chop it up as you go). Sprinkle the cooked meat with the flour and toss to coat, continuing to cook for another minute. Add the tomato paste, beef broth, Worcestershire, and minced rosemary, and stir together. Bring to a boil, then reduce the heat to low, cover, and simmer slowly for 10 to 12 minutes, until the sauce is thickened slightly.

Spread the filling evenly in a 9x13 pan. Top with the parsnip/carrot/potato goat cheese mash, starting around the edges to create a seal (which prevents the mixture from bubbling up) and then smooth toward the middle with a rubber spatula.

Bake for 25 minutes, or until the potatoes begin to brown. If you're worried about things bubbling over, you can place a parchment-lined sheet pan on the rack below it. Cool for 15 minutes before serving.