Onion Focaccia

INGREDIENTS

• 4 scallions, chopped fine
• 1 tablespoon freshly grated Parmesan
• 1 large yellow onion, sliced thin
• 1 large red onion, sliced thin
• 3 1/2 cups unbleached all-purpose flour
• 1/2 teaspoon sugar
• 1 cup lukewarm water
• 1 large shallot, sliced thin
• 1/2 teaspoon table salt
• a 1/4-ounce package (2 1/2 teaspoons) active dry yeast
• 1/4 teaspoon crumbled dried sage
• 6 tablespoons olive oil
• 1 teaspoon coarse salt, or to taste