In a large mixing bowl, combine warm water, yeast, and sugar. Let it sit for about 5 minutes until it becomes frothy.
Add the flour, salt, and 1/4 cup olive oil to the yeast mixture. Mix until a sticky dough forms.
Knead the dough on a floured surface for about 5-7 minutes until smooth and elastic. Alternatively, use a stand mixer with a dough hook for about 5 minutes.
Place the dough in a greased bowl, cover it with a damp cloth, and let it rise in a warm place for 1-2 hours, or until doubled in size.
Preheat your oven to 425°F. Grease a 13x18-inch baking sheet with olive oil.
Punch down the risen dough and transfer it to the prepared baking sheet. Stretch and press it out to fit the pan.
Use your fingers to create dimples all over the surface of the dough. Drizzle with olive oil and sprinkle with minced garlic, Parmesan cheese, rosemary, and coarse sea salt.
Let the dough rest for an additional 20-30 minutes while the oven preheats.
Bake for 20-25 minutes, or until golden brown. Allow to cool slightly before slicing.