Prepare the pastry: In a mixing bowl, combine 2 cups flour with 1/2 teaspoon salt. Cut in 10 tablespoons cold butter until mixture resembles coarse crumbs. Add 4-5 tablespoons ice water, mixing until dough comes together. Form into disk, wrap, and refrigerate 30 minutes.

Prepare the filling: Trim and halve 4 medium Belgian endives lengthwise. Heat 2 tablespoons butter in a large skillet over medium heat. Add endives cut-side down and cook 4-5 minutes until golden. Flip and cook 3-4 minutes more. Remove and set aside.

In the same skillet, add 1 tablespoon butter and sliced leeks (white and light green parts of 3 medium leeks). Cook over medium-low heat for 12-15 minutes, stirring occasionally, until very soft and lightly golden. Season with salt and pepper.

Preheat oven to 375°F. Roll out pastry on floured surface to 12-inch circle. Transfer to 10-inch tart pan, pressing into bottom and sides. Trim excess. Prick bottom with fork. Line with parchment and fill with pie weights. Blind bake 15 minutes.

While crust bakes, whisk together 4 eggs, 1 1/4 cups heavy cream, 1/4 teaspoon nutmeg, 1/2 teaspoon salt, and 1/4 teaspoon black pepper in a bowl.

Remove weights and parchment from crust. Spread cooked leeks evenly in crust. Arrange endive halves on top in spoke pattern. Sprinkle with 1 1/2 cups grated Gruyère cheese.

Pour egg mixture over vegetables, ensuring it fills all gaps. Bake 40-45 minutes until filling is set and top is golden brown. A knife inserted in center should come out clean.

Cool on wire rack for 15 minutes before slicing. Serve warm or at room temperature.