Lay squash slices out on a paper towel and sprinkle with salt. Let sit for 15 minutes.
Meanwhile caramelize onion by cooking over medium low heat in butter and olive oil, stirring occasionally, until soft and starting to caramelize, about 20-25 minutes. Add shallot and cook for 5 more minutes.
Lay dough round on a silpat or parchment paper lined baking sheet.
Squeeze out garlic from paper shell and spread it over dough, leaving a 1 inch border. Sprinkle with 1/2 of cheese.
Top with onion shallot mixture and then squash slices.
Season with salt and pepper and sprinkle with remaining cheese.
Fold dough up and over filling making pleats as you go around the edge.
Bake at 375 for 30-40 minutes or until golden.
Add onion topping** for the last 5 minutes of baking if desired. Cut into 4-6 wedges for serving