In a large skillet over medium heat, heat oil. Add garlic, anchovy if using, and red pepper flakes. Cook, stirring occasionally, until mixture is fragrant, 1 to 2 minutes.
Add whole tomatoes with their juices to the skillet, along with the butter. Season with salt and pepper and add basil sprig. Using a potato masher, or the back of a wooden spoon, crush tomatoes until a coarse sauce forms. Simmer for 25 minutes, continuing to crush larger pieces of tomato.
Remove basil, stir parm into tomato sauce, and make 6 wells in the sauce with a wooden spoon. Crack one egg into each well and cover skillet. Cook eggs to desired doneness, 2 to 3 minutes for set whites and runny yolks.
Remove from heat, season eggs with salt and pepper, and garnish with more cheese and torn basil. Serve with crusty bread for dipping.