Whisk together water and salt until combined.
To a stand mixer fitted with a dough hook, add the water mixture along with the bread flour. Mix on medium speed until a loose dough forms. Add the whole wheat flour and yeast, then continue mixing on medium speed for 7 minutes. To test that the dough is ready, pinch off a little piece and stretch it out. The dough should stretch thin enough that you can see light through the dough without any tearing. If the dough breaks right away, continue kneading. If at any time your mixer becomes too hot, take a break or begin hand kneading (see notes below).
Roll the dough into a tight ball, then place it in a lightly oiled mixing bowl. Cover with plastic wrap, and allow to rest for 1 hour.
Divide dough into five 9.9 ounces (280 grams) portions using a bench scraper. Roll each piece of dough into a tight ball. Place rolled dough balls into a lightly greased storage container roughly 3 inches (7 cm) apart from each other, and tightly secure with plastic wrap.
Store the dough in the refrigerator for 48 hours to develop flavor.
When you're ready to cook the pizza, remove the dough from the refrigerator, and allow it to come to room temperature. Arrange the oven rack to the center of the oven. Place a pizza stone on the rack, then heat oven to 450°F (230°C). Allow the oven and pizza stone to preheat for at least 30 minutes. Alternatively, heat pizza oven to 810°F (432°C).
Lightly flour a clean work surface. Pour some additional flour into a mixing bowl. Grab a dough ball with a bench scraper, place in the mixing bowl, and cover both sides in flour. Flatten one dough ball slightly with your hands, then use your fingers to make an indent for the crust. Once the dough is circular, use the outer palm of your hand to continue stretching the dough until it reaches a 13 inch (33 cm) circle with even thickness. To help stretch the dough, hang it on your knuckles, and allow gravity to pull it downwards.
Top the dough with tomato sauce and transfer with a pizza peel to a pizza stone dusted with cornmeal and bake for 10–14 minutes until the crust is golden brown. If you are using a pizza oven, bake for 60–90 seconds, rotating as needed, until the crust is golden brown and the bottom of the dough is fully cooked. Once the pizza comes out of the oven, while it’s still hot, top with fresh mozzarella, basil, and a drizzle of extra virgin olive oil. Repeat with remaining dough balls.