How to Make It
In a large saucepan, heat 1/4 cup of the olive oil until shimmering. Add the onions and cook over moderate heat, stirring occasionally, until softened, about 5 minutes. Add the vinegar, wine, sugar and a pinch of salt. Cover partially and cook over low heat, stirring occasionally, until the onions are very soft, about 20 minutes. Uncover and cook over moderate heat, stirring frequently, until browned, about 30 minutes longer; add water if the onions seem dry. Transfer the onion confit to a bowl and let cool.
Meanwhile, set a pizza stone on the bottom shelf of the oven. Preheat the oven to 500° for 30 minutes.
On a floured surface, roll out 1 ball of dough to a 14-inch round. Transfer to a pizza peel or cookie sheet dusted with cornmeal. Spread half of the onion confit over the dough to within 1 inch of the edge. Top with half of the tomatoes, Fontina, mozzarella, andouille and parsley. Lightly brush the edge with olive oil.
Slide the pizza onto the stone and bake for about 10 minutes, or until the crust is browned and the top is bubbling. Let cool for 5 minutes, then cut into wedges and serve. Meanwhile, repeat with the remaining dough and toppings. Alternatively, if you don't have a pizza stone, assemble the pizzas on lightly oiled baking sheets coated with cornmeal. Let rise for 30 minutes before baking directly on the sheet.