In a large skillet, heat the olive oil over medium heat. Add the onion and garlic. Cook, stirring occasionally, until softened, about 5 minutes.
Add the canned tomatoes, basil sprigs, salt, red pepper flakes, and black pepper. Stir, then bring to a simmer and cook, uncovered, until slightly thickened, 2 to 4 minutes.
Decrease the heat to medium-low. Using the back of a spoon, make 6 divots in the tomato mixture, spacing evenly apart. Crack an egg into a small bowl and carefully place one into each divot. Season the eggs with additional salt and pepper.
Cover the skillet with a lid and simmer until the egg whites are set but the yolks are still runny, 4 to 6 minutes. Uncover and remove the skillet from the heat. Sprinkle with parmesan cheese and garnish with additional basil. Serve immediately with good, crusty bread.
Notes
Use a stainless steel or enameled cast iron skillet. I don’t recommend seasoned cast iron or any other reactive metal pans, as the acid in the tomatoes can damage the pan or absorb a metallic flavor.
To check if your sauce is thick enough: When you make the wells in the tomato sauce for the eggs, look to see if they fill up with liquid very quickly. If they do, your sauce needs a couple more minutes to thicken up before you add the eggs.
Use freshly grated parmesan cheese. It melts better than the pre-shredded kind at the store.