In a large bowl, combine flour, sugar, yeast, and 3/4 teaspoon salt.
Warm 1/4 cup olive oil and water to 125–130°F. Add to the dry ingredients and stir until a soft dough forms.
Knead using a stand mixer with a dough hook for 2 minutes on low speed, or knead by hand for 8 to 10 minutes. Add up to 1/4 cup additional flour if dough is sticky.
Cover the bowl with a towel and let the dough rest for 10 minutes. Punch down gently.
Pour 1 tablespoon olive oil into a 10-inch cast iron skillet. Shape dough into a ball and place in the center of the skillet.
Cut a shallow criss-cross pattern on top of the dough.
Brush remaining olive oil over the dough. Mix garlic, rosemary, and remaining 1/2 teaspoon salt, then sprinkle evenly on top.
Cover and let rise for 1 hour, until slightly puffy.
Preheat oven to 400°F.
Bake for 20 to 25 minutes until golden brown. Remove from skillet and cool slightly on a wire rack.