Skillet Mushroom Thyme Flatbread Pizzas

Steps

1. Make the dough: in a large bowl whisk the flour, the yeast, the sugar and 8 g of the salt. Add the lukewarm water and 15 g of the olive oil and stir into a shaggy dough. This is about 65% hydration and 2% salt.
2. Knead the dough on a lightly floured counter for 8 minutes until smooth and springy. Return it to the bowl, cover, and let rise at about 75°F (24°C) for 1 to 1½ hours, until doubled in size.
3. While the dough rises, make the garlic oil: warm 35 g of the olive oil with the garlic and the red pepper flakes in a small pan over low heat for 4 to 5 minutes, until the garlic is pale gold. Take off the heat and let cool.
4. Cook the mushrooms: heat the remaining 15 g of olive oil in a large cast-iron skillet over medium-high heat. Add the mushrooms and cook without stirring for 3 minutes, then stir and cook 4 to 5 minutes more until browned and dry. Stir in the thyme, the remaining 2 g of salt and the black pepper, then move the mushrooms to a plate and wipe out the skillet.
5. Divide the risen dough in half, shape each half into a ball, cover and rest 15 minutes. Preheat the broiler with a rack about 6 inches below it.
6. Stretch one ball into a thin 11-inch flatbread. Heat the dry cast-iron skillet over medium-high heat until very hot, lay in the dough and cook 2 to 3 minutes until the bottom is browned in spots and bubbles rise on top.
7. Brush the top of the flatbread with half of the garlic oil, including half of the garlic slices. Scatter over half of the mozzarella, half of the mushrooms and half of the Parmesan.
8. Slide the skillet under the broiler for 2 to 4 minutes, until the cheese is bubbling and the crust edges are blistered and the center reaches about 200°F (93°C).
9. Slide the pizza onto a rack and repeat with the remaining dough, the remaining garlic oil, the remaining mozzarella, the remaining mushrooms and the remaining Parmesan.
10. Cool each pizza on a rack for 3 minutes, scatter with the fresh basil, then cut each into 6 slices.