Heat the olive oil in a 10-inch cast-iron skillet over medium-high heat. Add the sausage; cook, stirring occasionally, until browned and almost cooked through, 4 to 5 minutes. Add the onion and cook, stirring occasionally, until softened and slightly golden, 2 to 3 minutes.
Stir the bread into the sausage mixture and cook until lightly toasted, about 2 minutes. Add the marinara sauce and 2 cups water; bring to a simmer. Reduce the heat to medium (or move the skillet to a cooler part of the campfire). Stir in the provolone, 2 tablespoons Parmesan and 1/4 cup basil.
Use the back of a spoon to make 4 shallow wells in the tomato mixture; carefully crack 1 egg into each well. Cover the skillet and cook until the egg whites are set but the yolks are still runny, 4 to 9 minutes. Sprinkle with the remaining 2 tablespoons Parmesan and 1/4 cup basil. Season with salt and pepper.