Combine the water, yeast and 1 teaspoon of sugar in the bowl of a stand mixer and let stand for a few minutes or just until you see it start to foam.
Add the flour, remaining sugar, and salt. Stir by hand until well mixed, then add the olive oil. Stir well. Set the bowl on the mixer stand and knead with the dough hook for about 7 minutes stopping occasionally to scrape the side of the bowl. It will be a loose dough, but when you scrape it off the side it should have some snap to it.
With a heavy duty scraper, scrape dough into the center of the bowl. Cover the bowl and let dough rise for about 1 to 1 ½ hours. With instant yeast it should only take an hour.
Punch down the dough lightly and press the dough evenly into a well greased 7x11 inch pan. Cover and let rise again for about 30 minutes or until it is puffy and light. While the dough is rising in the pan, preheat the oven to 400 degrees F. and cook the onions.
In a large, lidded skillet, heat 1 tablespoon of olive oil. Add the onions and brown sugar and cook with the lid on for about 10 minutes. After 10 minutes remove the lid and continue cooking until onions are browned, seasoning with the salt and pepper.
After the dough has risen, oil your fingers and poke dimples aggressively all over the dough going almost to the bottom. Drizzle a tablespoon of olive oil over the focaccia dough letting it seep down into the holes.
Spread onions evenly over the top. Sprinkle with hazelnuts and rosemary.
Bake at 400 degrees F for about 28 to 30 minutes. Note: If you are used to baking focaccia at higher temperatures, this one bakes at a slightly lower temp (400) to keep the hazelnuts from burning and the onions from drying out too much.