Cut the onion into very thin slices. Finely mince the garlic.
In a large skillet, melt the butter and olive oil over medium heat. Add the garlic, zucchini and onions and cook until carmelized, about 20-25 minutes. Season with salt and pepper and remove from heat.
Preheat oven to 400 degrees. Roll out the puff pastry onto a parchment-lined baking sheet, smoothing the seams together until it measures about 9x13. Bake the pastry for 15 minutes and remove from oven. It will be puffed up high, so run a rolling pin over it to flatten it back out.
Layer 1/2 of the cheese, then the vegetables, then 1/2 of the cheese onto the pastry. Garnish with zucchini blossoms if you have them. Return to the oven for 10 more minutes. Slice and serve warm.