Oil 4 individual gratin molds. Season the chopped canned tomatoes with salt and pepper. If desired, stir roughly chopped garlic and/or sliced chilli into the tomato mixture. Spread the tomato mixture on the bottom of each mold. Scatter dried oregano on top. Arrange the sliced mozzarella in a wreath shape in each mold.
Bake in the middle of a preheated oven at 220°C (428°F) until the cheese begins to melt. Remove the molds from the oven. Crack 1 egg into the center of each mold, keeping the egg whole like a fried egg. Lightly season each with salt and pepper. Arrange the Parma ham strips on top. Immediately return to the hot oven and bake until the egg whites have set.
Sprinkle the chopped fresh basil on top and serve immediately.