Preheat oven to 500° And pizza stone in oven or grease a large baking sheet. On a lightly floured surface, roll one piece of dough out into an 8" circle, about ¼" thick. Spoon pizza sauce in middle of dough, then dot with ricotta and top with pepperoni and mozzarella.
Gently fold dough in half, dampen seams with water and pinch together, then crimp edges all around. Repeat with remaining dough. Transfer to prepared baking sheets. Brush tops with oil and sprinkle with salt. Using kitchen scissors or a sharp knife, slit tops in 2 to 3 spots to create steam vents.
Bake until tops are golden and filling is bubbling, 15 minutes, brushing with more oil halfway through. Let cool 5 minutes before cutting open.
Budino in Italian means pudding but this is more like a molten cake, moist and almost gooey in the middle when served warm from the oven. I like to serve the budino with a scoop of homemade Banana Chocolate-Chunk Ice Cream (in my cookbook, Cooking From the Hip), but it's also great with creme anglaise and fresh raspberries or strawberries.