Mixed Wild Mushroom Pizza with Fried Eggs

Mixed Wild Mushroom Pizza with Fried Eggs

Makes 4 individual pizzas

Ingredients
½ cup extra-virgin olive oil, plus more as needed
2 garlic cloves, finely minced
Semolina flour
Pizza Dough, dived into 4 balls (find recipe below)
1 cup freshly grated Parmigiano-Reggiano cheese
12 ounces fontina, diced (2 ¼ cups)
12 ounces fresh ricotta (1 ½ cups)
4 cups mixed fresh wild mushrooms, such as oyster, king oyster, shiitake, cremini, enoki, and chanterelle, thinly sliced fresh morels
¼ cup thinly sliced fresh morels
Kosher salt and freshly ground black pepper
4 large eggs

Procedure
Put a pizza stone or baking sheet on the lowest oven rack. Preheat the oven to 500 F. Let the stone get very, very, hot. 

In a small bowl, combine the oil and garlic.

Sprinkle a baking sheet with semolina flour. Pick up a dough ball with your fingers and gently pinch the edges of the ball while rotating it so that the dough stretches into a round. Drape the round over your knuckles and continue turning and stretching until the center is so thin its almost translucent. The dough should be about 9 inches in diameter. Gently place on the prepared sheet. Unless you have a very large pizza stone or baking sheet, you can probably make only 1 or 2 pizzas at a time. Keep the other dough rounds covered with plastic wrap until ready to use.

Spread a quarter if the Parmesan and fontina on the dough round, then crumble a quarter of the ricotta over the top. Scatter a quarter of the mushrooms over the cheese. Drizzle a quarter of the garlic oil all over the pizza and season with salt. Slide the sheet onto the hot stone and bake until the crust is browned and crisp, the cheese is melted, and the mushrooms are tender, about 15 minutes.

While the pizza bakes, heat a little oil in a small non-stick skillet over medium heat. Crack 1 egg into the skillet, lightly season with salt and pepper, and cook, sunny side up, until the white is just set and the yoke is runny. 
Grind pepper all over the pizza and slide the egg onto the pie. Repeat with the remaining ingredients, serving each pizza hot as it comes out of the oven.

Pizza dough
Makes about 1 pound, or enough for 4 individual pizzas
Ingredients
3 ¾ cups all-purpose flour, plus more for shaping
1 teaspoon active dry yeast
1 tablespoon kosher salt
Extra-virgin olive oil

Procedure
Combine the flour, yeast, salt, and sugar in a mixer fitted with the dough hook. Mix until just blended, then add 1 1/3 cups warm water. Mix until the dough comes together, then mix for another minute.

Lightly oil a large bowl. Transfer the dough to the bowl, lightly oil the top of the dough, and cover the bowl tightly with plastic wrap. Let rise in a warm spot for 8 hours or until the risen dough is marshmallowy.

On a lightly floured surface, use a bench scraper or sharp knife to divide the dough into quarters. With lightly floured hands, shape the pieces into balls by cupping the dough and turning it against the floured surface until round and tight.

Transfer the balls to a lightly oiled baking sheet or bowls, then lightly brush the tops with oil. Cover loosely with plastic wrap and let rise in a warm spot until tripled in volume, about 1 ½ hours. Use immediately or put a sheet of parchment on tip of the dough balls, then cover tight with plastic wrap. Refrigerate for up to two days. When ready to use, remove from the refrigerator and let stand un a warm place for 1 hour.