In a large skillet, heat 1 tablespoon extra virgin olive- oil over medium-low heat. Add the onions to the skillet and sprinkle 1 teaspoon of sugar over it. Stir occasionally and cook until tender (takes about 10-15 minutes
Place the dough on a parchment lined baking sheet. Pat and press the dough gently until the dough fills the pan completely. If the dough resists, let it rest for a few minutes before continuing (sometimes the dough can be moody). Cover the dough with a piece of plastic wrap and let it rise again until doubled in size (about 40-60 minutes).
Set a rack in the lower third of the oven and preheat to 425 F.
When the dough has doubled in size, remove the plastic wrap. Dimple the surface of the risen focaccia using your fingertips.
Brush on the remaining olive oil to the surface of the dough. Sprinkle on the sea salt (add the amount of salt you prefer. We like it a little saltier. Sprinkle on the chopped rosemary and caramelized onions.
Bake for 25-30 minutes, or until golden brown and puffed around the edges.
Remove from oven. Lift the focaccia from the pan with the parchment paper edges onto a cutting board. You’re supposed to let it cool a little on a rack before serving. That never happens over here. Brush on a little olive oil (the last tablespoon from the 4 tablespoons in the ingredient list) on the hot focaccia. Cut and serve.