Preheat the oven to 475°F and place a pizza stone or baking sheet inside to heat.
Heat 1 tablespoon olive oil in a large skillet over medium heat. Add the sliced onions and salt, then cook for 10 minutes until they soften and start to brown.
Pour in the balsamic vinegar and continue cooking for 5 more minutes until the onions turn glossy and most of the liquid evaporates. Remove from heat.
Roll the pizza dough into a 12-inch circle on a lightly floured surface. Brush the remaining tablespoon of olive oil over the dough.
Spread the balsamic onions evenly across the dough, leaving a small border around the edge. Sprinkle the mozzarella cheese on top and finish with black pepper.
Transfer the pizza to the hot stone or sheet and bake for 12 to 15 minutes until the crust is golden and the cheese bubbles.
Remove from the oven, let it rest for 2 minutes, then scatter fresh basil leaves over the top before slicing.