Light a grill. In a colander set over a medium bowl, toss the squash with the 1/2 teaspoon of salt; let stand for 15 minutes, then squeeze out the excess liquid.
In a large nonstick skillet, heat the 2 tablespoons of olive oil until shimmering. Add the squash and cook over moderately high heat just until golden in spots, 3 minutes.
In a food processor, pulse the tomatoes until almost smooth; season the tomato sauce with salt and the sugar.
On a lightly floured work surface, roll out the pizza dough to a 1/4-inch-thick round or oval. Brush the dough with olive oil and oil the hot grill grate. Drape the dough, oiled side down, onto the hot grate. Grill over moderate heat until marks appear on the bottom and the dough is slightly firm and puffed, about 3 minutes. Turn the dough over onto a cookie sheet and brush with olive oil. Spread the tomato sauce over the dough, leaving a 1-inch border. Scatter the squash over the pizza and top with the sliced mozzarella cheese and sausages.
Slide the pizza back onto the grill. Cover the grill and cook until the crust is done and the cheese is melted, about 5 minutes. Transfer the pizza to a platter, garnish with the peperoncini and basil and serve.
Bold southern Italian reds are a good match for sausage. Look for a concentrated, berry-rich bottle from Puglia.
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