Preheat the oven to 400 degrees F. Spray a baking sheet with nonstick cooking spray. If you have a pizza stone, put that in the oven, but leave a rack empty for baking the pizza rolls.
Roll out 1 pound of the pizza dough 1/8-inch thick on a floured work surface. Using a pizza cutter, trim the edges to make a 12-inch square. Starting about 1 inch from the bottom, spread the pizza sauce in a thin line, from the left side to the right. Top with a sprinkling of chopped spinach and a small sprinkling of shredded mozzarella cheese. Starting from the bottom, roll the dough over the filling, and then roll one more half turn. Using a pizza cutter, slice off the completed roll, forming a long tube shape. Then slice the tube into 1 1/2-inch pieces; pinch the cut ends to seal, forming little rolls.
Repeat the process with the remaining rolled out dough. You should be able to make about 22 rolls total. (You can freeze any leftover dough, or make some quick breadsticks.)
Place the rolls about 1 1/2-inches apart on the baking sheet and brush the tops with some of the egg wash. Bake until golden brown on top, 13 to 16 minutes. (And the cheese might be seeping out on the sides, which means you've done something right in life.)
While the pizza rolls bake, heat the butter and oil and in a medium skillet. Add the mushrooms and cook until tender, about 3 minutes. Season with salt and pepper.
Cut the remaining pound of pizza dough in half, and roll out each piece on a floured worked surface to make two roughly 8-to-10-inch rounds. Put the rounds on baking sheets, or use a pizza peel to build 1 pizza at a time if you are using a pizza stone.
Divide and spread the remaining pizza sauce evenly over both crusts. Follow with an even scattering of mushrooms, the whole spinach leaves and the remaining shredded mozzarella. Tear the bocconcini into pieces and scatter them over the tops of the pizzas. Bake both pizzas on the baking sheet or 1 at a time on the stone, until the dough is cooked through and the cheese is browned and bubbly, 13 to 17 minutes.
Top the pizzas with some torn prosciutto and basil leaves and good shavings of Manchego. Serve and inhale.