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1
In the bowl of an electric mixer fitted with the paddle attachment proof the yeast with the sugar in the water for 5 minutes, or until the mixture is foamy, add the flour, the salt, 3 tablespoons of the oil, and 1/2 cup of the Parmesan, and combine the dough well.
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2
With the dough hook knead the dough for 2 minutes, or until it is soft and slightly sticky.
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3
Form the dough into a ball, transfer it to an oiled bowl, and turn it to coat it with the oil.
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4
Let the dough rise, covered with plastic wrap, in a warm place for 1 1/2 hours, or until it is double in bulk.
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5
The dough may be made up to this point, punched down, and kept, covered and chilled, overnight.
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6
Let the dough return to room temperature before proceeding with the recipe.
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7
Press the dough evenly into a oiled jelly-roll pan, 15 1/2 by 10 1/2 by 1 inches, and let it rise, covered loosely, in a warm place for 1 hour, or until it is almost double in bulk.
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8
In a bowl stir together the remaining 1/4 cup Parmesan, the mozzarella, the Gorgonzola, the Fontina, the onion, and pepper to taste and sprinkle the mixture evenly over the dough.
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9
Drizzle the remaining 2 tablespoons oil over the cheese mixture and sprinkle the focaccia with the coarse salt.
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10
Bake the focaccia in the bottom third of a preheated 400F.
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11
oven for 35 to 45 minutes, or until it is golden brown, let it cool in the pan on a rack, and serve it warm or at room temperature.