This is another recipe inspired by the delicious, fresh mushrooms my dad gathers on his "mushroom hunts" at home in Northern California. At the peak of chanterelle season, we often have a surplus of the woody, flavorful mushrooms around the house and they pop up in everything from lasagnas to risotto to pizza. I couldn't find chanterelles at this time of year in New York City, but if you can get a hold of them, I would absolutely recommend adding them into this calzone for an extra level of flavor.
Heat the olive oil in a large pan over medium heat. Add the shallots and garlic and cook until the shallots are softened, about 5 minutes. Add the carrots and continue cooking, stirring occasionally, until the carrots are softened.
Add the mushrooms and cook for 3 minutes. Add the white wine and dried herbs, season with salt and pepper, to taste, and continue cooking until the wine has cooked off. Remove from the heat and set aside to cool slightly.
In a large mixing bowl, combine the cheeses. Once the mushrooms have cooled slightly, add them to the cheeses and stir to combine. Season with salt and pepper, to taste, and set aside.
Preheat the oven to 400 degrees.
Generously flour your work surface. Using a floured rolling pin, roll the pizza dough out into a 12-inch circle. Lightly brush the surface with olive oil. Transfer to a pizza stone or greased cookie sheet.
Top half of the dough with the mushroom-cheese mixture. (You may not need to use all of the mixture; you want there to be enough filling but not too much that the dough will stretch and break.) Wet the edges of the dough and fold over to form a calzone. Pinch the edges shut. Brush top of the dough with olive oil.
Bake until the calzone is golden brown, for about 20 minutes.