Combine the yeast, sugar, and ¼ cup (60ml) warm water in a large bowl. Stir gently, then let stand for 5–10 minutes until foamy and bubbly.
Add the remaining ¾ cup (180ml) warm water, olive oil, and salt to the yeast mixture, then stir in 2 cups flour and 1 tablespoon rosemary. Gradually add the remaining flour until the dough pulls away from the bowl but is slightly tacky.
Turn the dough onto a lightly floured surface and knead for 8–10 minutes by hand (or 5–6 minutes with a stand mixer on medium) until smooth, elastic, and springs back when poked.
Place the dough in a lightly oiled bowl, turn to coat, cover with a towel or plastic wrap, and let rise in a warm spot for 1 hour or until doubled in size.
Punch down the dough, divide into two equal portions, and shape each into an oval loaf about 8 inches long. Place seam-side down on a lined baking sheet, spacing at least 3 inches apart, and flatten slightly to about 1 inch thick.
Sprinkle the remaining 1 tablespoon rosemary over the loaves and gently press it in. Cover loosely and let rise 45–60 minutes until nearly doubled; preheat oven to 375°F (190°C) during the last 15 minutes.
Score 3–4 diagonal slashes across the top of each loaf, about ¼ inch deep, then bake on the middle rack for 15 minutes without opening the oven door.
Remove from oven, brush loaves generously with melted butter, and sprinkle with coarse sea salt. Return to oven and bake 10–15 minutes more until deep golden brown and hollow-sounding when tapped (internal temp 190°F–200°F / 88°C–93°C).
Transfer loaves to a wire rack and cool for at least 10 minutes before slicing to allow the interior to set properly.