Preheat oven to 400F; grease an 8 by 8-inch casserole dish with butter.
Add the butter to a medium saucepan over medium heat. Stir in the onion and cook until softened, but not browned, about 5 minutes, stirring occasionally. Add the garlic and cook 1 minute more, stirring constantly. Add the flour and cook 1 minute. Whisk in the milk, Dijon, Worcestershire, paprika, salt, and pepper, and bring to a simmer, whisking frequently. Turn off the heat and whisk in the cheese a handful at a time until smooth.
Spread the mashed potatoes in the bottom of the prepared dish. Spread the chopped turkey evenly on top of the mashed potatoes, and then spread the broccoli evenly on top of the turkey. Top with the cheese sauce, and spread it out evenly as best you can.
Let the casserole cool slightly (this is so that the puff pastry isn’t going on top of hot sauce, which may cause it to not rise properly).
Unwrap the thawed puff pastry and place it on top of the casserole, tucking the sides down into the dish. Brush a little eggwash on top (there will be extra – do not try to use it all), and cut a few slits in the top of the puff pastry for the steam to vent.
Bake until the pastry is puffed and golden, about 25 to 30 minutes. Cool slightly before cutting and serving.