In the bowl of a stand mixer fitted with the paddle attachment, combine sourdough starter and water. Mix on low until soupy.
Add flour, salt, and sugar, and mix, starting on low and increasing speed to medium until the batter pulls away from the sides of the bowl, about 5-7 minutes.
Cover bowl and let rise until doubled, about 2 hours.
Place a baking stone on the middle rack of your oven and preheat to 450°F.
Heavily dust a work surface with flour and turn out dough. Divide dough in two, and fold up the corners to tighten the dough. Flip and transfer to a floured piece of baking parchment.
Brush top of bread with olive oil, sprinkle with rosemary leaves, black pepper, and kosher salt.
Use a pizza peel to slide onto the baking stone, and bake until golden browned on the top, about 15 minutes.