Line a sheet tray with parchment paper and grease with a thin layer of olive oil.
Place sugar and 1 1/2 cups water into the bowl of a stand mixer fitted with the dough hook. Sprinkle the yeast over the top. Let the mixture stand for 10 minutes to activate the yeast.
Combine the bread flour, all-purpose flour, salt and the tablespoon rosemary in a large bowl. Add to the mixer along with the oil. Knead the dough on medium speed until it forms a smooth, supple ball that is not sticky to the touch, about 5 minutes. Turn the dough out on the prepared sheet tray, drizzle with olive oil and cover with a bowl or clean kitchen towel. Allow to rise until it doubles in size, about 2 hours.
Using oiled fingertips, gently press the dough out onto the sheet tray, making dimpled indentations all over the dough. Cover with a towel and allow to rise again for another 45 minutes.
Preheat the oven to 425 degrees F.
Sprinkle the dough with the onions, olives and rosemary and drizzle generously with oil. Bake the focaccia until it is puffed and golden brown, 20 to 25 minutes. Drizzle with additional olive oil and sprinkle with sea salt flakes before serving.