Preheat oven to 425°F.

In a large bowl combine the warm water and yeast. Lightly stir and allow to rest for about 5 minutes. Add the salt, sugar, 1 tablespoon olive oil and flour. Mix with a wooden spoon until it comes together into a shaggy dough. Add a bit more water, a little at a time, if the dough is too dry. Turn out onto a lightly floured work surface and knead for about 5 to 7 minutes until it is smooth and elastic. Return the dough to the mixing bowl, that has been greased and turn it over to coat both sides. Cover with plastic wrap, loosely, and a damp kitchen towel. Set in a warm place to double in size, about 1 hour.

In the meantime, prepare the other toppings. Separate the Brussels sprout leaves and throw them onto a baking sheet. Drizzle with 1 tablespoon olive oil and season with ½ teaspoon salt and ½ teaspoon black pepper. Toss to evenly coat and roast in the oven for about 10 to 15 minutes, or until the leaves are crispy. Remove from oven and allow to cool.

Sauté the diced red onion in 1 tablespoon olive oil and season with remaining ½ teaspoon salt and ½ teaspoon black pepper, for about 5 minutes, or until translucent and slightly browned. Allow to cool down.

In a small pot heat the remaining (¼ cup) olive oil with the whole garlic cloves and rosemary sprigs. Cook on low for about 5 to 10 minutes to develop the flavor. Remove from heat and allow to cool down.

Cut the dough in half and roll out each half on a lightly floured work surface. Roll into a large thin circle. Place each rolled pizza crust onto two baking sheets. Brush the crusts liberally with the garlic herb infused oil. Bake for about 5 to 7 minutes or until just beginning to brown. Sprinkle each dough with the mozzarella and pecorino cheese, dividing it among both crusts. Top with the crispy Brussels sprouts, and sautéed onions. Lay a couple slices of pancetta on each pizza. Bake for about 5 minutes to melt the cheese and continue to brown the crust.

Remove the pizzas from the oven and crack two eggs onto each pizza. Return to the oven and continue to cook for another 5 minutes (for runny yolks). Remove from the oven and cut into wedges. Serve warm or at room temperature. Enjoy!