Preheat the oven to 425 degrees F. Line a baking sheet with parchment paper. Place the sheet of puff pastry on the parchment. Poke a few holes with a fork in the pastry center. This helps keep the center from bubbling up too much!
Cover the puff pastry with about three quarters of the fontina cheese, leaving a ½-inch border along the outsides. Top the fontina with the sliced brussels and minced garlic. Sprinkle on a pinch of salt and black pepper. Sprinkle on the rest of the fontina. Sprinkle on the pistachios.
Brush the edges of the pastry with the egg wash. Bake the pastry for 20 to 25 minutes, until the pastry is slightly puffed and golden and the cheese is bubbly. Let cool for a minute then slice and serve!