Set a pizza stone on the bottom of the oven and preheat the oven to 500° for 30 minutes. Meanwhile, in a medium saucepan, cover the potatoes with water and bring to a boil. Simmer over moderate heat until the potatoes are just tender, about 20 minutes. Drain and let cool, then slice 1/8 inch thick.
In a large skillet, heat 1 tablespoon of the olive oil. Add one-third of the yellow squash in a single layer and season with salt and pepper. Cook the squash over moderately high heat, turning once, until golden brown, about 2 minutes. Transfer to a plate. Repeat with the remaining 2 tablespoons of olive oil and squash in two batches.
Generously flour a pizza peel or a large rimless baking sheet. On a lightly floured work surface, roll out 1 piece of pizza dough into a 12-inch round, 1/8 inch thick. Transfer the round to the pizza peel and top with one-fourth of the potato slices. Drizzle lightly with olive oil and season with salt and pepper. Arrange one-fourth of the squash over the potato, then scatter one-quarter of the tomatoes followed by one-quarter of the Manchego on top.
Transfer the pizza to the hot stone and bake for about 7 minutes, or until the crust is golden and the cheese is bubbling. Transfer the pizza to a work surface and cut into wedges. Top the wedges with some of the torn frisée and serve at once. Repeat with the remaining dough and toppings.