Special equipment: a 14-inch pizza pan
For the dough: Combine the flour, rosemary, yeast, sugar and 1 teaspoon salt in a food processor and pulse to combine. Add 3/4 cup warm water and the oil and process until the dough forms a ball. Transfer to a large, lightly oiled bowl and cover with plastic wrap. Let stand in a warm, draft-free place until doubled in size, about 1 1/2 hours.
For the topping: Meanwhile, preheat the oven to 400 degrees F.
Toss the squash with 1/2 tablespoon of the olive oil, 1/4 teaspoon salt and pepper to taste. Roast until just tender, about 10 minutes.
In a small saucepan over medium-low heat, add the remaining 2 tablespoons olive oil and the sage, rosemary, red pepper flakes and garlic. Heat for 1 to 2 minutes, just to infuse the oil.
Sprinkle cornmeal or flour on a 14-inch pizza pan and set aside.
Liberally flour a clean work surface. Place the dough on top and use your hands to stretch it out into a 14-inch circle. Carefully lay the dough on the pizza pan. Brush the infused oil onto the dough. Top with the mozzarella and the roasted squash, leaving a 1-inch border around the edge. Bake the pizza until the crust is golden brown, 14 to 18 minutes. Carefully sprinkle the goat cheese evenly on top.
Toss the arugula with the 2 teaspoons olive oil, lemon zest and juice and a pinch of salt and black pepper. Top the pizza with the arugula, then cut into slices to serve.