Sourdough Mushroom Flatbread Pizzas with Mozzarella

Steps

1. Day 1, morning: feed your sourdough starter with equal weights of flour and water and leave it at about 75°F (24°C) for 4 to 8 hours, until it has doubled, is domed and bubbly, and has peaked.
2. In a large bowl, stir the peaked sourdough starter into the water, then add the bread flour and mix until no dry flour remains. Cover and rest 30 minutes.
3. Sprinkle 9 g of the salt (nearly all of it; save the rest for the mushrooms) and 15 g of the olive oil over the dough and squeeze and fold them in until smooth. This dough is about 67% hydration and 2% salt, counting the flour and water in the starter.
4. Bulk rise covered at about 75°F (24°C) for 4 to 5 hours. During the first 2 hours, do 4 sets of stretch-and-folds 30 minutes apart. The dough is ready when it has grown about 50%, looks airy and jiggles when the bowl is shaken.
5. Divide the dough into 2 equal pieces, shape each into a tight ball, and place them in lightly oiled covered containers. Cold proof in the fridge overnight, 12 to 24 hours.
6. Day 2: make the sauce. Warm 10 g of the olive oil in a small saucepan over medium heat, add half the garlic and cook 30 seconds. Stir in the tomato paste, canned tomatoes, oregano and red pepper flakes and simmer 10 to 15 minutes until thick. Cool.
7. Make the mushrooms: heat the remaining 15 g of olive oil in a skillet over medium-high heat, add the mushrooms and cook undisturbed 4 minutes, then stir in the remaining half of the garlic, the thyme, the remaining 1 g of salt and the black pepper and cook until browned and dry, about 4 minutes more.
8. Take the dough balls out of the fridge 1 to 2 hours before baking; they should be soft, puffy and spring back slowly when poked.
9. Place a baking stone or upside-down sheet pan on the middle rack and preheat the oven to 500°F (260°C) for at least 45 minutes.
10. On a floured sheet of parchment, press and stretch one dough ball into an oval flatbread about 1/4 inch thick, leaving a slightly thicker rim.
11. Spread half the tomato sauce over the dough, scatter on half the mozzarella, then half the mushrooms, then sprinkle with half the Parmesan.
12. Slide the pizza on its parchment onto the hot stone and bake 10 to 12 minutes, until the crust is deep golden and blistered and the cheese is bubbling and spotted brown. Repeat steps 10 to 12 with the second dough ball and the remaining halves of the sauce, mozzarella, mushrooms and Parmesan.
13. Let each pizza rest on a rack 3 minutes, scatter half the parsley over each, and cut each into 6 slices.