In the bowl of a stand mixer fitted with the flat beater attachment, combine the flour, salt, and black pepper. Add the cold diced butter and shortening, tossing them gently with a fork to coat with the flour mixture. Mix on medium-low speed until the mixture resembles coarse cornmeal, with small pea-sized pieces of butter remaining. Gradually add the ice water, mixing on low speed until the dough begins to come together. Shape the dough into a flat disk, wrap it in plastic wrap, and refrigerate for at least 30 minutes.

Preheat the oven to 375°F (190°C). Transfer the chilled dough onto a lightly floured surface and roll it out to a 1/4-inch thickness. Carefully fit the dough into a 9-inch tart pan, pressing it into the fluted edges and trimming any excess dough. Line the tart shell with aluminum foil and fill it with dried beans or pie weights. Bake for 25 minutes, then remove the weights and foil. Return the tart shell to the oven and bake for an additional 5 minutes until lightly golden. Allow the tart shell to cool to room temperature.

Using a mandoline or a sharp knife, slice the yellow squash, zucchini, and red bell peppers into 1/8-inch thick rounds. Slice the red onion into thin half-moon shapes.

Evenly distribute the shredded goat cheese and sliced basil over the bottom of the cooled tart shell. Arrange the vegetable slices around the outer edge of the tart, overlapping two slices each of yellow squash, zucchini, and red bell pepper, followed by three slices of red onion. Continue layering smaller circles of vegetables toward the center, using squash slices to cover the middle.

Drizzle the assembled tart with extra-virgin olive oil and season with salt and freshly ground black pepper to taste. Bake in the preheated oven for approximately 30 minutes, or until the vegetables are tender and the tart shell is golden brown around the edges.

Allow the tart to cool slightly before slicing. Serve warm or at room temperature as a main dish or appetizer.