1 large Hass avocado
1 tablespoon finely chopped cilantro
1 1/2 teaspoons lime juice
1/8 teaspoon salt
1/2 pound pizza dough, homemade or store-bought (see Recipe Note)
4 large eggs
1 tablespoon vegetable oil
Hot sauce, for serving (optional)
Cut the avocado in half lengthwise, remove the pit and, with a large spoon, scoop the flesh into a medium bowl. Add the cilantro, lime juice and salt. Mash with a fork until smooth, with a few chunks of avocado. Taste and adjust seasoning. (Depending on the size of your avocado, you may need more salt or lime juice.) Set aside.
Divide the dough into 4 equal pieces. On a well-floured cutting board, roll each piece into a thin 6-inch circle. (If the dough keeps springing back as you roll it, let it rest for a few minutes to relax the gluten and try again.)
Heat a well-seasoned cast iron skillet (see Recipe Note) over medium-high heat until very hot. Place one of the dough circles in the center of the skillet. Cook for 1 to 2 minutes, until the underside is browned and the top surface is bubbly. Flip and cook other side until browned, pressing down with a spatula if the dough puffs up off the bottom of the pan. It may be charred in spots, which is fine. Transfer to a plate and repeat with remaining dough circles.
Spread 1/4 of the avocado mixture onto each cooked piece of dough.
Heat the oil in a skillet over medium heat. (If using the same skillet you used for the dough, first let it cool slightly and clean out any burned flour that may be sticking to it.) Fry eggs to desired doneness and place each one on top of a pizza. Serve immediately, with or without a drizzle of hot sauce.