Cremini and Shiitake Mushroom Pizza Recipe

Name: Cremini and Shiitake Mushroom Pizza Recipe
Ingredients: 1/2 recipe rustic country pizza dough, halved and formed into two balls; 1 lb. cremini mushrooms; 1 lb. shiitake mushrooms; 3 or 4 cloves garlic; 1 shallot; Peanut oil or another neutral oil; Kosher salt; Freshly ground black pepper; 2 or 3 sprigs fresh thyme leaves, stripped from stems; 2 Tbsps. unsalted butter; About 6 oz. crushed San Marzano tomatoes or premium plum tomatoes; 1 lb. fresh mozzarella; Parmigiano-Reggiano; Extra virgin olive oil; Coarse sea salt