In a food processor, pulse the flour, 5 tbsp. cubed butter and 1/4 tsp. salt until crumbly. Add the ice water and pulse until a dough forms; transfer to a floured surface. Knead the dough twice, then form into a disk; wrap and refrigerate for 1 hour.
Transfer the dough to a floured surface; roll into an 1/8-inch-thick round. Transfer to a 9-inch pie plate. Trim the overhang to 1/2 inch; crimp the edges. Refrigerate for 30 minutes. Position a rack in the center of the oven and preheat to 375 degrees .
Remove the tart shell and prick it all over with a fork. Line the inside with foil; fill with pie weights (or dried rice or beans) adn bake for 20 minutes. Remove the weights and foil and bake again until fully cooked, about 10 minutes. Let cool.
Rinse the sliced leeks in cold water. In a medium skillet, melt the remaining 2 tbsp. butter over medium heat. Add the leeks; cook until soft, 5 minutes.
In a bowl, whisk the cream, eggs, remaining 3/4 tsp. salt and the pepper.
Distribute the leeks and cheese in the cooled shell. Pour the cream mixture on top. Bake for 20 minutes. Remove, transfer the oven rack to the top shelf, then bake again until set, 15 minutes. Transfer to a rack; let rest for 10 minutes.