Onion Confit:
Heat olive oil in heavy bottomed saucepan. Add onions, stirring to coat with oil and separate rings.
Cook until soft over low heat, 5 to 8 minutes. Add vinegar, wine, salt and sugar. Stir; bring to a boil. Place lid on pan slightly askew; lower heat to simmer and cook for 30 minutes, stirring occasionally. Remove lid, keeping at simmer, and continue cooking 30 additional minutes, or until onions are very soft and liquid is reduced. Do not brown or scorch. Remove from heat; set aside.

Pizza:
Preheat oven to 425°F. If using pizza stone, place in cold oven and preheat. If using dough, roll into a 12- to 14-inch circle or a rectangle. Place on cookie sheet to transfer to stone or on a pizza pan. Brush edges of dough with olive oil. Spread the onion confit over the dough or prepared crust, leaving a 1/2-inch bare edge. Sprinkle with Fontina cheese. Sprinkle tomatoes and andouille rounds evenly on top. Sprinkle Mozzarella cheese over all. Slide onto pizza stone or place baking pan in oven. Bake pizza about 10 minutes, or until golden brown. Sprinkle hot pizza with Parmesan cheese and parsley.