In a medium bowl, combine warm water (about 105–115°F / 40–46°C) with the sugar and sprinkle the active dry yeast over the surface. Stir gently, then let sit 5–10 minutes until foamy and fragrant.

In a large mixing bowl (or the bowl of a stand mixer fitted with the dough hook), whisk together the all-purpose flour and salt. Make a well in the center.

Add the foamy yeast mixture and 3 tablespoons extra-virgin olive oil to the flour. Mix by hand with a wooden spoon until it comes together into a shaggy dough. If using a stand mixer, mix on low for 1–2 minutes.

Turn the dough out onto a lightly floured surface and knead by hand for 8–10 minutes until smooth and elastic. If using a stand mixer, knead on medium for 6–8 minutes. The dough should be slightly tacky but not sticky; add up to 1 tablespoon more flour if excessively sticky.

Shape the dough into a ball and place it in a lightly oiled bowl. Cover with plastic wrap or a clean kitchen towel and let rise in a warm draft-free place until doubled, about 1 to 1¼ hours.

Filling & Assembly

While the dough rises, prepare the mix-ins: chop the pitted Kalamata olives into roughly 1/4" pieces, thinly slice (chiffonade) the basil leaves, mince the garlic, and grate the Parmesan. Combine the chopped olives, sliced basil, minced garlic, grated Parmesan, black pepper, and red pepper flakes (if using) in a small bowl. Stir to distribute evenly.

When the dough has doubled, gently deflate it on a lightly floured surface. Roll or stretch it into a rectangle roughly 12 x 8 inches and about 1/4–1/2 inch thick.

Evenly scatter the olive-basil mixture over the dough, leaving a 1/2-inch border. Press the mixture lightly into the dough so it adheres but does not tear the dough.

Starting from the long edge, roll the dough tightly into a log. Pinch the seam closed and tuck the ends under to form a loaf shape. Transfer the loaf seam-side down to a parchment-lined baking sheet or a lightly oiled 9x5-inch loaf pan.

Cover the shaped loaf loosely with oiled plastic wrap or a towel and let it proof until puffy and nearly doubled, about 30–45 minutes.

Bake & Finish

About 20 minutes before baking, preheat the oven to 375°F (190°C). Position a rack in the center.

Just before baking, brush the top of the loaf with 1 tablespoon extra-virgin olive oil and sprinkle the coarse sea salt evenly over the top.

If desired, score the top with 2 or 3 shallow diagonal slashes (about 1/4 inch deep) to control expansion.

Bake on the center rack for 25–30 minutes, or until the crust is golden brown and the loaf sounds hollow when tapped on the bottom. An instant-read thermometer inserted into the center should read about 190–200°F (88–93°C). If the top browns too quickly, tent loosely with foil for the last 5–10 minutes.

Remove the loaf from the oven and transfer to a wire rack. Let cool at least 20 minutes before slicing so the crumb sets. Garnish with fresh basil leaves, if using.