Preheat oven to 375 degrees. Have ready a 14-by-4 1/2-inch bottomless rectangular tart form or one with a removable bottom on a parchment-lined baking sheet. On a lightly floured surface, roll pate brisee dough into a 7-by-16-inch rectangle. Fit the dough into the mold, and trim the sides flush with the top of the mold. Transfer the shell to the freezer to chill for 20 minutes.
Remove the shell from the freezer, prick bottom with a fork, and line with parchment paper cut to fit. Fill with dried beans or metal pie weights. Bake until the crust is just beginning to brown, about 15 minutes. Remove from the oven, and remove beans or weights. Return the crust to the oven, and bake until golden brown, about 10 minutes more. Remove from the oven, and set aside on a wire rack.
Using a mandoline or vegetable peeler, very thinly slice 1 green zucchini and 1 yellow squash lengthwise. Place slices in a colander in a single layer, and sprinkle lightly with salt. Place colander in a bowl, and set aside to drain for 30 minutes.
Cut the remaining zucchini and squash into 1/3-inch dice. In a large skillet, melt butter over high heat. Add leeks and diced squash, and season with salt and pepper. Cook until golden brown but still firm, about 8 minutes. Evenly distribute cooked vegetables in the crust. Sprinkle Gruyere on top.
Place salted squash slices between double layers of paper towels. Gently press down to remove as much liquid as possible. Alternating squash colors, weave a lattice pattern over the top of the cheese and vegetables, covering the entire surface. Trim or tuck in ends to fit.
In a medium bowl, whisk together egg, egg yolk, and cream, and season with salt and pepper. Lift the edges of the lattice in several places, and pour in the egg mixture. Using a pastry brush, coat the lattice with olive oil. Bake, loosely covered with aluminum foil, until the custard is set, 30 to 35 minutes. Remove lattice tart from oven, and place on a wire rack to cool slightly before serving.