Lightly dust a work surface and the dough with flour (just enough to keep the dough from sticking). Flatten the dough with the palm of your hand and carefully knead and stretch until it is about 8 inches in diameter (you can also use a rolling pin, if preferred).
Line a baking sheet with parchment paper and transfer the dough to the baking sheet. Spread the pizza sauce around the dough, leaving room for the crust. Top evenly with the cheese and scatter the mushrooms and shallots on top.
Place in the oven and bake until the cheese is bubbly and the crust is golden, about 18-20 minutes. Remove from the oven and let cool slightly before scattering the basil leaves on top. Season generously with freshly ground black pepper.