Grilled NY Pizzas with Parmesan, Mushrooms and Thyme

Steps

1. Make the dough first: in a large bowl whisk the bread flour, instant yeast, sugar and 10 g of the salt. Add the lukewarm water and 20 g of the olive oil and mix until no dry flour remains, about 63% hydration and 2% salt.
2. Knead the dough 8 to 10 minutes until smooth and elastic. Cover and let rise at about 75°F (24°C) for 1 1/2 to 2 hours, until doubled in size.
3. While the dough rises, make the sauce: simmer the canned tomatoes, tomato paste, half of the garlic, the oregano and 1 g of the salt in a small pot for 15 minutes until thick, then cool.
4. Cook the mushrooms: heat 10 g of the olive oil in a skillet, add the mushrooms and cook until browned and dry, about 8 minutes. Stir in the remaining half of the garlic, the thyme, the remaining 1 g of salt and the black pepper; set aside.
5. Divide the risen dough in half, shape into balls and rest, covered, 30 minutes, until they spring back slowly when poked. Meanwhile heat the grill to high, about 500°F (260°C), and set up one cooler zone.
6. Stretch one ball into a 12-inch round. Brush the top with a quarter of the brushing oil and lay it oiled side down on the hot grate; grill 2 to 3 minutes until marked and puffed.
7. Flip the crust onto the cooler zone, brush with another quarter of the brushing oil, and quickly spread on half of the sauce, half of the mozzarella, half of the mushrooms and half of the Parmesan.
8. Close the lid and grill 4 to 6 minutes until the cheese melts and the bottom is crisp. Repeat with the second dough ball, the remaining brushing oil, sauce, mozzarella, mushrooms and Parmesan.
9. Scatter the parsley over both pizzas, rest 3 minutes on a rack, then cut each into 6 slices.