This is a two-pot affair if you're cooking for 4 persons. Use your frying pan for the veggies and then transfer to your pots.
Heat oil over medium heat. Add the sliced garlic, anchovies and red-pepper flakes and cook just until the garlic turns golden brown at the edges, about 1 minute. Stir in tomatoes, salt, pepper and basil paste and rosemary. and turn the heat to medium-low.
Simmer, squashing tomato pieces with a spoon, until the tomatoes break down and thicken into a sauce, 20 to 25 minutes. Stir in Parmesan, butter, salt and red-pepper flakes to taste.
Using your ladle, make indentations for your eggs in the tomato sauce, then crack an egg into each indentation. Cover the pan and let cook until the eggs are set to taste, about 2 to 3 minutes for runny yolks. (If the pan is not covered, the eggs won't cook through, so don't skip that step.)
To serve, sprinkle more Parmesan, then spoon into into bowls. Serve with toast.