Peel the potatoes and carrots 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, uncover, decrease the heat to maintain a simmer and cook until tender and easily crushed with tongs, approximately 15 to 17 minutes. Drain the potatoes in a colander and then return to the saucepan. Mash the potatoes and then add the butter, milk, goat cheese and mash until smooth. Salt and pepper to taste. I added 3/4 teaspoon salt and 1/2 teaspoon freshly ground pepper.
Preheat the oven to 400 degrees F. While the potatoes are cooking, prepare the filling. Place the canola oil into a 12-inch saute pan and set over medium high heat. Once the oil shimmers, add the brussels sprouts, carrots and onions and sauté just until they begin to take on color, approximately 3 to 4 minutes. Add the garlic and stir to combine. Add the pork and sirloin, salt and pepper and cook until browned and cooked through, approximately 3 minutes. Sprinkle the meat with the flour and toss to coat, continuing to cook for another minute. Add the tomato paste, beef broth, Worcestershire, rosemary and stir to combine. Bring to a boil, reduce the heat to low, cover and simmer slowly 10 to 12 minutes or until the sauce is thickened slightly.
Spread the mixture evenly in a 8-inch square dish. Top with the carrot goat cheese mash, starting around the edges to create a seal to prevent the mixture from bubbling up and smooth with a rubber spatula. Place on a parchment lined half sheet pan on the middle rack of the oven and bake for 25 minutes or just until the potatoes begin to brown. Remove to a cooling rack for at least 15 minutes before serving.