In a small bowl, combine the tomatoes, 1 teaspoon of the olive oil, and basil. Season with salt and fresh ground pepper to taste, and briefly set that deliciousness aside.
Using a cookie/biscuit cutter or mason jar lid, remove a circle (ideally 2-3 inches in diameter) of bread from each slice.
Heat a large skillet (preferably cast iron) over medium-high heat. When hot, add the remaining tablespoon of olive oil and swirl to coat the bottom of the pan. Add the bread slices and rounds to the pan and cook for about 3 minutes until the undersides are golden brown.
Flip the bread over and reduce the heat to medium. Crack each egg into a small ramekin and gently pour them into the holes in the bread slices. Immediately sprinkle the bread (including the rounds) and egg with mozzarella. (I avoided sprinkling cheese on the yolk so I could have maximum yolk porn for the photos, but you do you.) Cover the pan with a lid and cook for 3-4 minutes until the whites of the eggs are set (but the yolks are still runny!) and the cheese has melted.
Carefully transfer each egg-in-the-hole to a plate, leaving the bread rounds in the pan. Return the heat to medium-high and flip the rounds over so that they are cheese-side down. Cook for about 30 seconds until the cheese has browned slightly. (Once it has browned the cheese will release itself from the pan.) Remove from the pan.
Season each egg-in-the-hole with a little salt and pepper and top with the tomato-basil mixture. Add the cheesy rounds to each plate and drizzle everything with balsamic reduction (if using). Serve immediately.