Heat the olive oil in a cast iron skillet. Add the chorizo, stirring occasionally, until browned and almost cooked through, (6 to 10 minutes).
Add the onion and cook until softened and golden, (2 to 3 minutes).
Add the marinara sauce and 2 cups of water; bring to a simmer. Reduce the heat to medium and stir in the pepperjack, 2 tablespoons parmesean, and ¼ cup of the basil.
Make 4 shallow wells in the tomato mixture, carefully cracking an egg into each one.
Cover the skillet and cook until the egg whites are set but the yolks are still runny. Sprinkle with the remaining parmesean cheese and basil. Season with salt and pepper.
Serve with sliced Italian for dipping and enjoy!