Mix the diced tomatoes and the tomato paste together in a bowl to make a tomato sauce. Chop the basil.
Heat the olive oil in an oven safe skillet (I used a grill pan) over medium heat. Add the tomato sauce, and the basil, and bring to a slow but steady simmer.
Use a spoon to create spots for the eggs to sit in the sauce. Then crack the eggs into these spots. Add the mozzarella, and let cook for 4 minutes.
While the eggs are cooking in the sauce, prepare the garlic bread. Melt the butter and stir in the garlic. Then spread the butter and garlic mixture on both sides of the slices of bread. Place on a baking sheet.
After about 4 minutes of simmering in the sauce, the eggs should be about ⅔ cooked. The bottom of the whites should be cooked, but the tops will still be raw.
Turn the oven's broiler on, and place an oven rack in middle of your oven. Place the skillet with the eggs in the oven. I find this method of cooking the eggs lets the top of the whites cook, while keeping the yolks runny. Keep an eye on the eggs, they will be ready in 2-3 minutes, once the whites are solid.
Remove the skillet with the eggs from the oven. Move an oven rack to the top, and place the garlic bread under the broiler to toast. Keep on eye on it, it will only need about 30-60 seconds per side to toast.
Serve the eggs in purgatory right away, with a side of garlic bread.