Heat 1 tablespoon oil in a medium skillet over medium heat. Add shallot; cook, stirring occasionally, until softened, about 3 minutes. Add zucchini; cook, stirring occasionally, until light golden and liquid has been released, about 5 minutes. Transfer to a large bowl; set aside.
Halve one-third of the tomatoes. Stir halved and whole tomatoes, cheeses, basil, lemon zest, flour, and sugar into shallot-zucchini mixture. Season with salt and pepper. Set aside.
Roll out dough on a lightly floured surface to a 13-inch circle, about 1/4-inch thick. Make seven 3-inch-long cuts around edge of dough, evenly spacing. Trim to make 7 rounded flaps. Transfer to a 10-inch pie plate. Drizzle crust with remaining tablespoon oil. Spread with filling. Fold in flaps of crust, slightly overlapping. Put tomatoes on the vine in center. Refrigerate until cold, about 20 minutes.
Preheat oven to 375 degrees. Whisk cream and egg yolk in a small bowl. Brush crust with egg wash. Bake pie on a rimmed baking sheet until crust is golden brown and juices are bubbling, about 45 minutes.