Place the potatoes in a large saucepan and cover with water. Bring to a boil, then salt the water. Cook until the potatoes are tender, 13-15 minutes. Drain, and set aside to cool.

In a small saucepan, combine 3/4 cup plus 3 tablespoons of the cream, the garlic and the nutmeg. Bring to a boil. Cook until it is reduced by half, then season with salt and pepper.

In a saute pan, melt the butter. Add the leeks and cook until softened, about 5 minutes. Remove the leeks from the heat and stir in the parsley.

Whisk the egg yolk with the remaining tablespoon of cream. Lightly flour a surface, and roll out the puff pastry into two 13×6-inch rectangles. Set one of the rectangles on a parchment lined baking sheet. Place half of the potatoes on the pastry, leaving a half inch border, overlapping the potatoes. Layer on half the leeks and half the cheese. Season with salt and pepper. Repeat the layers with the remaining potatoes, leeks and cheese. Brush the edges of the dough with the egg wash, then place the second rectangle of puff pastry on top. Gently press the edges to seal. Cut 2-inch slits crosswise in the center of the crust, 2 inches apart, to let the steam escape. Brush the top of the pastry with the remaining egg wash. Cover, and refrigerate for about 30 minutes.

Preheat the oven to 400F. Bake the pie until it is golden brown and puffy, about 35 minutes. Remove from oven. Pour the cream mixture into the pie vents with a funnel. Bake for an additional 10 minutes. Remove to a wire rack and let sit for 10 minutes before serving.