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, the garlic, and nutmeg to a boil in a small saucepan over medium-high heat. Cook mixture until reduced by half. Season with salt and pepper; set aside.
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. Set aside.
Preheat oven to 400 degrees. Whisk egg yolk and remaining tablespoon cream in a small bowl; set aside. Divide puff pastry on a lightly floured surface into two 6-by-13-inch rectangles. Set 1 rectangle on a baking sheet lined with parchment paper. Add half of the potatoes, leaving a 1/2-inch border all around and overlapping potatoes slightly. Top with half of the leek mixture and 3/4 cup cheese; season with salt and pepper. Repeat layering with remaining potatoes, leeks, and cheese. Brush edges of dough with egg wash. Cover with remaining dough 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. Refrigerate until cold, about 30 minutes.
Bake pie 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.