Step 1

Preheat the oven to 375 degrees F. Use 1 tablespoon of the butter to grease a 9-by-13-inch baking dish. Set the dish on top of a sheet pan and set aside.

Step 2

In a large sauté pan over medium heat, heat 1 tablespoon of the olive oil until shimmering. Add the turkey and cook, breaking up any larger pieces, until almost fully browned, about 5 minutes. Add the fennel, garlic powder, onion powder, sage, thyme, 1 teaspoon salt and 1/2 teaspoon black pepper. Stir to combine, cook for another 1 to 2 minutes, and then remove the turkey from the pan to a plate.

Step 3

Add the remaining tablespoon olive oil to the pan along with the mushrooms. Cook until browned and their water has released, about 5 minutes. Season with 1/2 teaspoon salt and a pinch of pepper. Transfer the mushrooms to the plate with the turkey.

Step 4

Add the remaining 4 tablespoons butter to the pan and cook until melted and starting to bubble. Add the onions and cook until translucent and lightly browned, about 5 minutes. Stir in the Brussels sprouts and sweet potatoes, 1 1/2 teaspoons salt and 1/2 teaspoon pepper. Cook until the sweet potatoes start to soften and the sprouts start to wilt, 4 to 6 minutes. Add the flour and cook, stirring to cook out the rawness, about 1 minute. Add the broth and scrape up the browned bits at the bottom of the pan. Add the heavy cream and simmer until slightly thickened, 8 to 10 minutes. Adjust the seasonings.

Step 5

Return the turkey and mushrooms to the pan and stir to combine. (If your pan is too small, you can also pour the sauce into the prepared baking dish and stir in the turkey and mushrooms.) Transfer the mixture to the prepared baking dish. Top the baking dish with the sheet of puff pastry, allowing the sides to hang over the edge of the dish. Using a pastry brush, brush the egg wash all over the top of the pastry. Use a paring knife to cut vents in the top of the pastry.

Step 6

Bake until the pastry is puffed and golden brown, 40 to 50 minutes. Remove from the oven and let stand for 10 minutes before serving.