Slice the mozzarella into 1/4 inch thick pieces. If it’s incredibly watery fresh mozzarella (all brands vary), you may want to let it sit on a paper towel to remove moisture for about 15 minutes then dab the mozzarella with the paper towel to remove any additional moisture.
Slice the olives in half. Thinly slice the chili pepper (keep the seeds).
When the oven is ready, dust a pizza peel with cornmeal or semolina flour. (If you don’t have a pizza peel, you can use a rimless baking sheet or the back of a rimmed baking sheet. But a pizza peel is well worth the investment!) Stretch the dough into a circle; see How to Stretch Pizza Dough for instructions. Then gently place the dough onto the pizza peel.
Use the back of a spoon to spread a thin layer of pizza sauce across the dough. Top with mozzarella cheese, saving out a small bite for tasting. Taste a bite of the mozzarella cheese; if it does not taste salty, add a pinch or two of kosher salt to the pizza. (The pizza has olives, which also adds saltiness.) Top the cheese with the sliced olives and chili peppers.
Transfer the pizza to the pizza stone using the pizza peel, then bake until the cheese is melted, about 7 minutes in the oven (or 1 minute in the pizza oven).
Remove from the oven and allow to cool for minutes, then top with torn basil leaves. Slice into pieces and serve immediately.