Heat oven to 400 degrees.
Pour enough sea salt onto cooking tray to be able to hold the potatoes, place the potatoes on the salt and bake until done; approximately 20-25 minutes.
Mix together the Basil, Tomatoes and chopped Mozzarella. Drizzle with half the olive oil, mix thoroughly and season with salt and pepper.
When the potatoes are done, remove them from the oven and cut an X into the top of each one; squeeze the potato to open it up.
Place a heaping tablespoon of the mozzarella, basil and tomato mixture into each potato, drizzle each with a bit of the remaining olive oil, season with salt and pepper and serve hot.