Whisk together the flour, instant yeast, 1 teaspoon of kosher salt, and sugar in a large bowl until combined.
Add warm water and 3 tablespoons of olive oil to the dry ingredients. Knead with a dough hook on medium speed for 5-6 minutes, or by hand for 8-10 minutes, until the dough is smooth and slightly sticky.
Transfer the dough to an oiled bowl, turning to coat. Cover with plastic wrap and let rise in a warm place for 1 to 1.5 hours, until doubled in size.
Pour 2 tablespoons of olive oil into a 9x13-inch pan and spread evenly across the bottom and up the sides.
Gently punch down the dough and transfer it to the prepared pan. Use your fingertips to press and stretch the dough toward the edges, resting for 10-15 minutes if it resists.
Drizzle 1 tablespoon of olive oil over the top, cover loosely, and let rise for 45 minutes to 1 hour until puffy and pillowy. Preheat oven to 425°F (220°C) during the last 15 minutes.
With well-oiled fingertips, press deep dimples across the entire surface of the dough, nearly to the bottom of the pan.
Scatter fresh rosemary, flaky sea salt, and black pepper evenly over the top. Drizzle with remaining olive oil.
Bake in the center rack for 20-25 minutes, rotating once, until the top is golden brown and the edges pull away from the pan.
Rest in the pan for 5 minutes, then transfer to a wire cooling rack. Cool for 10-15 minutes before slicing and serving warm.