For the Pizza Dough:
½ cup warm water (about 110 degrees)
1 envelope (2¼ teaspoons) instant yeast
1¼ cups water, at room temperature
2 tablespoons olive oil
4 cups bread flour
1½ teaspoons salt
For the Toppings:
1 tablespoon unsalted butter
1 lb. cremini mushrooms, sliced
¼ of a red onion, thinly sliced
1 cup pesto (homemade or store-bought)
8 ounces provolone cheese, shredded
½ cup grated Parmesan cheese
1. Make the Pizza Dough: Measure the warm water into a 2-cup liquid measuring cup. Sprinkle in the yeast and let stand until the yeast dissolves and swells, about 5 minutes. Add the room temperature water and oil and stir to combine.
2. Process the flour and salt in a large food processor, pulsing to combine. Continue pulsing while pouring the liquid ingredients (holding back a few tablespoons) through the feed tube. If the dough does not readily form a ball, add the remaining liquid and continue to pulse until a ball forms. Process until the dough is smooth and elastic, about 30 seconds longer.
3. Turn out the dough onto a lightly floured work surface. Knead by hand for a few strokes to form a smooth, round ball. Put the dough into a deep oiled bowl and cover with plastic wrap. Let rise until doubled in size, 1 to 2 hours. Press the dough to deflate it.
4. Assemble the Pizza: Place a pizza stone on a rack in the lower third of the oven (if using). Heat oven to 500 degrees for at least 30 minutes.
5. While the oven is preheating, prepare the mushrooms and onions. In a skillet, melt the butter over medium heat and add the sliced mushrooms and onions. Cook, stirring occasionally with a wooden spoon, until the mushrooms have released all of their liquid and both the mushrooms and onions are soft and browned, 10 to 15 minutes. Set aside.
6. Turn the dough out onto a lightly floured work surface. Divide the dough into two pieces. Form each piece of dough into a smooth, round ball and cover it with a damp cloth. Let the dough relax for at least 10 minutes but no more than 30 minutes. (You only need one ball of dough for this recipe, so at this point you can wrap one ball of dough in plastic wrap, put in a ziploc bag and freeze for another day - just move it to the refrigerator the morning you plan to use it).
7. Flatten the dough ball into a disk using the palms of your hands. Starting at the center of the disk and working outward, use your fingertips to press the dough until it is about ½-inch thick. Holding the center in place, stretch the dough outward. Rotate the dough a quarter turn and stretch again. Repeat until the dough reaches a diameter of 12 inches. Use your palm to press down and flatten the thick edge of the dough.Transfer your prepared pizza dough to a pizza peel, parchment-lined baking sheet or pizza pan (whichever you are using).
8. Spread the pesto over the pizza dough, just as you would pizza sauce, leaving a ½-inch border uncovered. Spread the mushroom and onion mixture evenly over the pesto, and then top with the provolone and Parmesan cheeses. Slide the dough onto the heated stone, or place your baking sheet or pizza pan into the oven.
9. Bake until the crust edges brown and the cheese is golden brown in spots, 8 to 12 minutes. Remove from the oven, slice and serve (be careful, it will be hot!).