Preheat the oven to 400°F (If using a baking stone/steel, place it on a rack in the bottom third of the oven before you start preheating). Line a large rimmed baking sheet with parchment paper.

Place the tomatoes, squash, garlic, and shallot on the prepared baking sheet, drizzle with olive oil (just to coat), and season with salt and pepper. Gently turn the vegetables to coat them in the oil, then spread everything out in as even a layer as you can.

Roast the vegetables for 30 minutes or until the squash and garlic are tender and the tomatoes have begun to brown in spots. Remove from the oven and let cool slightly.

Increase the oven temperature to 500°F (if using a baking sheet) or as high as it will go (if using a baking stone/steel).

While the roasted tomato-squash mixture cools, make the herb oil: Using a mortar and pestle, grind together the basil, rosemary, 4 tablespoons of olive oil, a generous pinch of salt, and a grind or two of black pepper until the herbs are mostly broken up.

If using a baking stone/steel, set your oven to Broil on high.

Stretch or roll out your dough to a 12-inch circle, then transfer it to an oiled baking sheet or a lightly floured pizza peel (if using a baking stone/steel).

Brush the herb oil lightly all over the dough, trying not to let it pool up too much in any one spot. Arrange the roasted vegetables in a thin layer on the dough (you might have some veggies left over), then top with the mozzarella. Sprinkle with the ground sumac, followed by the shredded Gouda or Gruyère.

Transfer the pizza to the oven and bake until the crust is golden and the cheese has browned in spots, 8 to 10 minutes on the baking sheet, 6 to 8 minutes on the baking stone/steel.

Remove the pizza from the oven. Top with some torn fresh basil leaves; slice and serve.