In a large mixing bowl, combine the warm water, sugar, and yeast. Let it sit for about 5 minutes until it becomes frothy.
Add the flour, salt, and ¼ cup olive oil to the yeast mixture. Stir until a dough forms.
Knead the dough on a floured surface for about 5-7 minutes until smooth and elastic.
Place the dough in a greased bowl, cover it with a damp cloth, and let it rise in a warm place for about 1 hour, or until it doubles in size.
Preheat the oven to 425°F.
Once the dough has risen, punch it down and transfer it to a greased baking sheet. Press it out into a rectangle about ½ inch thick.
In a small bowl, mix the minced garlic with a tablespoon of olive oil. Brush this mixture over the dough.
Sprinkle the grated Parmesan cheese, chopped rosemary, and coarse sea salt evenly over the top.
Use your fingers to create dimples all over the surface of the dough.
Let the dough rest for an additional 20 minutes while the oven heats.
Bake for 20-25 minutes, or until golden brown. Remove from the oven and drizzle with a little more olive oil before serving.