Combine warm water and cane sugar in the bowl of a stand mixer fitted with the dough hook. Sprinkle in the yeast and stir once more. Let the mixture sit for approximately 5 minutes, until the surface becomes foamy. If no foam appears, discard and start anew with fresh yeast.

Incorporate the flour and sea salt into the yeast mixture. Begin mixing on low until a coarse dough forms, then increase the speed to medium and continue kneading for 5 minutes. The dough should become soft, sticky, and elastic, clinging slightly to the sides of the bowl.

Coat a large bowl with 2 tablespoons of olive oil. Using a spatula, transfer the dough from the mixer to the oiled bowl—handling by hand is not advised due to its stickiness. Gently spread any oil that pools along the bowl's edge over the top of the dough. Cover with a damp cloth or plastic wrap and let it rest until doubled in size, about 1 to 1½ hours.

Grease a 9x13-inch baking dish with another 2 tablespoons of olive oil. Lightly oil your hands, then uncover the dough and fold it inward from the edges using your fingertips, working around the bowl to shape it into a rough ball.

Place the dough into the oiled pan and turn it gently to coat. Press it out toward the edges; if it contracts, allow it to rest before pressing again. Cover the dish and leave the dough to rise for 45 minutes or until it has doubled. Preheat the oven to 425°F after 30 minutes of this rise.

Once risen, uncover the dough. Drizzle the final 2 tablespoons of olive oil across its surface. Rub oil onto your fingers, then dimple the dough thoroughly by pressing all the way down to the pan. If desired, scatter flaky salt and chopped rosemary over the top. Bake for 20 to 30 minutes, or until the bread achieves a rich golden hue.