Soak the olives in cool water to cover for at least 20 minutes and up to 1 hour to remove the excess salt. Drain and blot dry before adding them to the dough.
In a stand mixer fitted with the dough hook, combine the flour and the sugar. Add the yeast, water, and salt and mix on low speed until the dough becomes smooth, elastic, and very springy, 8 – 10 minutes.
Transfer the dough to a lightly oiled bowl, turn to coat, cover with plastic wrap or damp towel, and let rise in a warm place until nearly doubled in size, about 30 minutes. Add the olives to the bowl. Fold the dough over on itself, pressing gently to release the gas, and repeat the folding until the olives are evenly distributed. Cover the dough and let rest until relaxed, about 30 minutes.
Turn the dough out onto a lightly floured work surface and round it into a smooth ball, pulling the outer layer taut and pinching the excess dough together at the base of the ball. Leave the dough seam side down on the floured work surface, cover it with a cloth, and let rest for 15 minutes.
To finish shaping the dough, turn it seam side up and stretch it into a square. Fold the square in half from top to bottom, pressing lightly with your fingertips to tighten the outer layer of the dough. Fold the dough in half again, this time from side to side, and seal the 2 edges together. Round the dough, forming a taut outer surface, and place seam side up in a bowl or round basket lined with a floured, clean flat-weave cloth. Cover loosely.
Let the dough rise until it has nearly doubled in size and the dough springs back slowly to the touch but does not collapse, 1 hour.
Preheat the oven to 425°F. Line a baking sheet with parchment paper.
Turn the dough out seam side down onto the prepared baking sheet. Brush or mist the bread lightly with water. Cut a shallow X into the top of the loaf. Bake until the crust is crisp and well browned and the loaf sounds hollow when thumped on the bottom, 25 – 30 minutes. Let cool completely on a wire rack before slicing and serving.