In a bowl of a stand mixer with the dough hook attachment, combine warm water (110 to 115 degrees F), yeast, and sugar. Stir to combine and let sit for 10 minutes until foamy. See more about proofing yeast here.
Add 4 cups of the flour, salt, olive oil, and Kosher salt to the yeast mixture, and mix/knead at low speed to combine. Increase to medium speed, and continue mixing/kneading until dough is smooth and elastic, about 6-8 minutes. If too sticky, add the remaining ¼ cup flour.
Remove dough from bowl and shape dough into a ball with your hands. Oil a large bowl with olive oil. Place the dough in the bowl, making sure to coat the dough with the oil. Cover with bowl with plastic wrap and let rise in a warm place for 1 hour, or until doubled in size.
Once dough has doubled in size, oil a 15in x10in sheet pan with more olive oil, about 2 tablespoons. Dump the dough onto the prepared sheet pan. Using all your fingers, stretch to a rectangle, turning the dough over a few times to make sure both sides are covered with oil.
Deliberately, with all your fingers, press down almost all the way down to the bottom of the pan (yes, you heard me!) without creating large holes.
Cover the dough with plastic wrap again, and let rise for 1 hour in a warm and draft-free place.
While dough is rising, preheat oven to 425 degrees F.
Remove plastic wrap. Drizzle more olive oil (I know, it’s a lot!) on the dough, about 2-3 more tablespoons. Sprinkle the top evenly with rosemary and 1/2 teaspoon flaked sea salt.
Bake until golden brown, about 20 minutes on the middle rack. Remove from oven and brush with more olive oil, and let cool for 10-15 minutes before serving. Enjoy!