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1
Heat 2 tablespoons of the olive oil in a large saute pan over medium heat until hot.
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2
Add the onions, season with salt so the onions release their liquid, and reduce the heat to medium-low.
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3
Cook until the onions stop releasing water and the pan is nearly dry again, about 4 minutes.
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4
Do not allow the onions to brown.
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5
Add the water, stir, cover, and cook until softened, about 10 minutes.
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6
Uncover, stir in the thyme, and cook over medium heat until the onions are light brown, about 10 minutes longer.
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7
Season lightly with pepper.
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8
Do not cook the onions too long now as they will brown further in the oven.
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9
Let cool for several minutes.
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10
Preheat the oven to 500 degrees F. Dust 2 baking sheets with cornmeal.
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11
Cut the dough into 3 equal pieces.
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12
Working on a floured surface, shape each piece of dough by hand or with a rolling pin into an 8-inch round, keeping the edges a little thicker than the center.
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13
Transfer the rounds to the prepared baking sheets.
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14
Brush each round with 1 teaspoon of the olive oil and divide the onions evenly among them.
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15
Let rise for about 20 minutes.
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16
Push the dough with your fingers.
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17
Top each round with the caramelized onions and then scatter olives on top.
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18
Dot rounds evenly with the cheese.
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19
Bake until light brown all around the edges and on the bottom, about 12 minutes.
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20
Let cool for a minute, then, if desired, pile a handful of parley leaves on top of each.
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21
If using, put the vinegar in a spray bottle and mist the parsley.
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22
Chef's Note: Diced cooked potatoes are also a good addition to the onions.
