Preheat the oven to 500°F (if using a baking sheet) or as high as it will go (if using a baking stone/steel; place the stone/steel in the bottom third of the oven before you start preheating). Let the oven preheat for at least 30 minutes. Then, if you’re using a baking stone or steel, switch the oven to Broil on high.
Bring a medium pot of water to a boil. Add the butternut squash and cook for 8 minutes or until fork tender. Drain well.
In a small bowl, whisk ⅓ cup of the coconut milk with the fish sauce, lime juice, and sugar until the sugar is completely dissolved.
Heat the oil in a medium saucepan over medium-high heat until it starts to shimmer. Add the onion and cook until soft and translucent, about 4 minutes, then add the garlic, ginger, and Thai chile. Sauté for 30 seconds or until aromatic. Add the curry paste and 1 tablespoon of coconut milk to the pan and sauté for 2 minutes, then stir in the coconut milk–fish sauce mixture, butternut squash, and tofu. Cook the curry for 3 to 5 minutes to let the flavors blend and the sauce thicken. Remove the pan from the heat and set it aside to cool slightly.
Stretch or roll out your dough to a 12- to 14-inch circle, then transfer it to an oiled or parchment-lined baking sheet or a lightly floured pizza peel (if using a baking stone/steel).
Scoop the curry onto the dough and spread it out evenly, leaving a 1-inch border of dough all around. Drizzle 1 tablespoon of the remaining coconut milk over top.
Transfer the pizza to the oven and bake until the crust is golden and the tofu 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.
As soon as the pizza comes out of the oven, drizzle it with the remaining tablespoon of coconut milk and sprinkle on the chopped cilantro. Let it rest for 5 minutes, then slice and serve with sriracha on the side.