In a medium bowl, stir together 1 cup warm water, sugar, and yeast. Let stand until mixture is foamy, about 5 minutes.
In the bowl of a stand mixer fitted with the paddle attachment, combine flour and salt. With mixer on low speed, add yeast mixture and 2 tablespoons oil, beating just until combined. Switch to the dough hook attachment. Beat at medium speed until dough is smooth and elastic, about 7 minutes.
Spray a large bowl with cooking spray. Place dough in bowl, turning to grease top. Cover and let rise in a warm, draft-free place (75°) until doubled in size, about 1 hour.
Drizzle 2 tablespoons oil each into 2 (9-inch) cast-iron skillets.
Lightly punch down dough. Add 2 tablespoons rosemary, kneading until combined. Divide dough in half, and place in prepared skillets. Press dough into bottom of skillets. Cover and let rise in a warm, draft-free place (75°) until doubled in size, about 45 minutes.
Preheat oven to 375°. Using your fingertips, press dough to create divots. Sprinkle with remaining 2 tablespoons rosemary, and drizzle with remaining 2 tablespoons oil.
Bake until golden brown, about 20 minutes. Garnish with sea salt and pepper, if desired.
Recipe by Taste of the South at https://www.tasteofthesouthmagazine.com/rosemary-focaccia/