In the bowl of a stand mixer fitted with the dough hook attachment combine the oil, yeast and water. Let stand until the yeast is dissolved, about 5-8 minutes.
To make the Focaccia:
In another mixing bowl whisk together the flour and salt. With the mixer running on low speed slowly add in the flour. Mix until a smooth, supple dough forms, about 8-10 minutes. Transfer the dough to a bowl brushed with olive oil. Brush the ball of dough with more oil Cover with plastic wrap and set aside to rise for 1 hour or until doubled in volume. Punch down the dough.
Preheat the oven to 475 degrees.
Add 1/4 cup of the oil to a 12 inch round pan and spread it evenly, making sure you coat the bottom and sides of the pan.
Spread the dough to the edges of the pan with your fingers, starting from the center and working your way out.
Add the onions and drizzle the remaining oil over them. Sprinkle the rosemary over the entire surface of the focaccia, followed by a sprinkle of salt as desired.
Cover with plastic wrap and set aside to rise in a warm place for 1 hour. Bake for 30-35 minutes.