In a medium skillet, heat 1 tablespoon of olive oil over medium heat. Allow the oil to warm up and shimmer, which should take about 1-2 minutes.
Add the chopped onion to the skillet and sauté until it becomes translucent, about 5 minutes. Stir occasionally to prevent sticking.
Once the onions are softened, add the minced garlic and red pepper flakes to the pan. Cook for an additional 1-2 minutes, stirring frequently until fragrant.
Pour in 1 cup of tomato sauce, followed by the kosher salt and black pepper. Stir everything together and let it simmer for about 5-7 minutes.
Using the back of a spoon, make small wells in the sauce for the eggs. Carefully crack each egg into a well, ensuring they remain intact.
Cover the skillet and let the eggs cook for about 5-8 minutes, or until the whites are set but the yolks are still runny.
Once the eggs are cooked to your liking, sprinkle the chopped parsley and grated parmesan cheese over the top.
Serve the Eggs in Purgatory hot, straight from the skillet, paired with crusty bread or toast.