Add yeast, warm water, and sugar to the bowl of a stand mixer. Let sit for 5–10 minutes until foamy.
Add flour and salt and mix on low until a loose, slightly sticky dough forms.
Switch to the dough hook and knead for 15 minutes, adding more flour as needed to prevent sticking.
Grease the bowl with 2 tablespoons of olive oil, return the dough, and let rise in a warm spot for 1 hour or until doubled in size.
Oil your hands and fold the dough over itself 6–8 times, rotating the bowl each time.
Brush 2 tablespoons of olive oil into a 9x13 baking dish. Spread the dough evenly into the pan, pressing to the edges. Let rise for another hour.
While the dough rises, heat the minced garlic in the remaining olive oil over low heat until soft and translucent.
Preheat oven to 425°F. Oil your hands and press dimples all over the surface of the dough. Spread the garlic mixture on top, sprinkle with sea salt, and add rosemary.
Bake for 25–30 minutes until the top is golden brown.
Let cool, remove from the pan, and slice into 12 pieces.