Slice onions finely.

Heat olive oil or butter in large frying pan at medium low. Add onions. Season with salt and pepper. Cook covered, stirring often, until caramelized (45 minutes). Do not let burn. Let cool.

In a small bowl combine goat cheese and milk until paste is spreadable.

Line baking sheet with parchment paper. Sprinkle Parmesan cheese on the parchment paper.
Carefully untoll the defrosted puff pastry over the grated cheese. Using a knife, make a slight cut 1/2 inch from the borders all around the pastry sheet without cutting through. Always keep puff pastry as cool as possible and handle it as little as possible.

Pierce pastry lightly with a fork to make small holes that will let steam escape during baking.
Place a piece of parchment paper within cuts. Put pie weights on top and par-bake for 6 minutes.
Remove from oven. Remove weights and peel top parchment paper. Return pastry to oven for 3 minutes. Remove.

Spread goat cheese within cut borders. Top with cooled caramelized onions.

Bake for 8 minutes. Remove from oven. Peel bottom parchment paper.

Add basil or arugula, drizzle with balsamic vinegar, and sprinkle salt to taste.