Remove dough from refrigerator and let warm up slightly, about 30 minutes or so.
Oil a rimmed baking sheet with the basil flower oil, spreading with your fingers or a pastry brush to cover the entire surface. Alternatively, you can also use a 13×9-inch pan for this (you'll get a slightly thicker final bread).
Remove dough from bowl with oiled hands and place on baking sheet, flipping to coat with olive oil. Use your fingers to gently stretch and flatten the dough just a little bit. You don't want to stretch it to fit the pan at this point – just let it rest for now.
Cover with an inverted sheet pan or well-oiled plastic wrap and let the dough rest at least an hour. Press the dough gently to flatten and stretch it slightly. If using a rimmed baking sheet, it still won’t fill the pan. This is totally fine!
Leave the dough to rest again another 2-4 hours, or until doubled and bubbly. This may take a while depending on your sourdough starter and your room temperature.
Preheat oven to 425° F.
Use the fingers of both your hands to dimple the dough (as if you're planning the piano), pressing your fingers all the way to the sheet pan. Dimple entire surface of dough, stretching very gently as you go but being careful not to tear the dough.
Arrange tomatoes and mozzarella balls all over the dough, pressing them into the dough slightly.
Drizzle additional basil flower oil over bread and toppings. Sprinkle with coarse sea salt, if desired.
Bake for 25-30 minutes, until bread is golden brown on the top and bottom. Allow to cool at least 10 minutes, then sprinkle fresh basil leaves** over bread. Let bread cool at least another 30 minutes before slicing and serving.