Peel the onions and then slice into super thin rounds.
In a sauté pan over high heat add 2 tablespoons of olive oil and the sliced onions. Add a heavy pinch of salt, stir well and cook for about 5 minutes, stirring once.
After 5 minutes, turn the heat down to medium and let cook under brown and caramelized. This could take up to 45 minutes. Stir them every 10 minutes or so to make sure the onions are cooking evenly. Once cooked, remove from pan and set aside.
Assemble and Bake Tart
To assemble the tart you'll need to have your puff pastry defrosted, but still cold. Take out of the freezer and let rest 30-45 minutes on the counter. In the meantime, preheat the oven to 425 degrees.
Roll out the puff pastry just a bit and place on a parchment lined baking sheet. Then layer the caramelized onions over the top, leaving a small edge of puff pastry uncovered. Then sprinkle the goat cheese over the top of the tart.
Now, fold all of the edges over until you have a rustic tart shape. Then put into the oven and bake until the puff pastry is golden brown and puffed up, about 20-25 minutes.
Notes
You can easily double this recipe. Just use twice the number of onions and caramelized them in a large sauté pan with tall sides. Then you can use both pieces of puff pastry that typically come in a box. Remember to keep an eye on the onions as they start to brown, so they don't go from perfectly caramelized to burnt when you turn your back.