In the large bowl of an electric mixer fitted with the dough hook stir together the yeast, the sugar, and 1 3/4 cups lukewarm water and proof the yeast mixture for 5 minutes, or until it is foamy. Stir in 4 1/2 cups of the flour, the salt, and 2 tablespoons of the oil and knead the dough, scraping down the dough hook occasionally and adding as much of the remaining 1/2 cup flour as necessary to form a soft, slightly sticky dough, for 3 minutes. Transfer the dough to a lightly oiled bowl, turn it to coat it with the oil, and let it rise, covered, in a warm place for 1 hour, or until it is double in bulk. Knead in the chopped rosemary, press the dough with lightly oiled hands into a well-oiled 15 1/2- by 10 1/2-inch jelly-roll pan, and let it rise, covered loosely, for 30 minutes. The dough may be made 8 hours in advance and kept covered and chilled.

Dimple the dough with your fingertips, making 1/4-inch-deep indentations, brush it with the remaining 1 tablespoon oil, and top it with the onion, the olives, the salt, and the whole rosemary leaves. Bake the focaccia in the bottom third of a preheated 400°F. oven for 35 to 45 minutes, or until it is golden and cooked through. Transfer the focaccia to a rack, let it cool for 10 minutes, and serve it, cut into squares, warm or at room temperature.