This stunning, savory pie is made of puff pastry wrapped around a potato, leek, and Comté-cheese filling. Perfect as a hearty appetizer or vegetarian main, it is made to win the hearts and warm the stomachs of your party guests.
Cover potatoes with water in a medium saucepan. Bring to a boil over high heat. Add a pinch of salt; cook until just tender, 13 to 15 minutes. Drain. Let cool.
Bring 3/4 cup plus 3 tablespoons cream, garlic, and nutmeg to a boil in a small saucepan over medium-high heat. Cook until mixture is reduced by half. Season with salt and pepper.
Melt butter in a skillet over medium heat. Add leek; cook, stirring occasionally, until softened, about 5 minutes. Remove from heat. Stir in parsley; season with salt and pepper.
Preheat oven to 400°. Whisk egg yolk and remaining 1 table- spoon cream in a small bowl; set aside. On a lightly floured surface, divide puff pastry into two 6-by-13-inch rectangles. Set one rectangle on a baking sheet lined with parchment. Top with half of potatoes, leaving a 1/2-inch border all around and overlapping slightly, then half of leek mixture and 3/4 cup cheese; season with salt and pepper. Repeat layering with remaining potatoes, leek mixture, and cheese. Brush edges of pastry with egg wash. Cover with remaining pastry rectangle; gently press edges with a fork to seal. Cut 2-inch slits lengthwise in center of crust, 2 inches apart. Brush with egg wash and sprinkle with parsley sprigs. Refrigerate until cold, about 30 minutes.
Bake until golden brown and puffy, about 35 minutes. Remove from oven; pour cream mixture into pie vents with a funnel. Bake 10 minutes more. Let stand 15 minutes before serving.