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.
Cook the sausage in a small skillet over medium heat, breaking it up with a wooden spoon until it is no longer pink, about 5 minutes. Remove the pan from the heat and transfer the sausage to a paper towel–lined plate to drain.
Melt the butter in a medium saucepan over medium heat and add the 2 whole sage leaves. Cook for 1 to 2 minutes, until the sage begins to curl, then use tongs or a slotted spoon to remove the sage from the butter. Stir in the pumpkin, garlic, cream, vinegar, ⅛ teaspoon of the red pepper flakes, and ¼ cup of the pecorino. Stir until the sauce is heated through, 2 to 3 minutes. If the sauce is too thick, stir in 1 to 2 tablespoons of water or reserved pumpkin juice. Remove the pan from the heat and set it aside to cool.
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).
Spoon the cooled sauce onto the dough disk and spread it evenly, leaving a ½-inch border of dough. (You will need about ¾ cup of sauce to cover the dough, but you'll have plenty more if you want a saucier pizza.) Scatter the cooked sausage over the sauce, and top with the remaining ¼ cup of pecorino cheese and the remaining ⅛ teaspoon of red pepper flakes.
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 and let it cool for at least 5 minutes, then scatter the sliced sage over top; slice and serve.