Preheat your oven to 400°F (200°C).

In a mixing bowl, toss the peeled and cubed butternut squash with 1 tablespoon of olive oil, salt, and pepper until evenly coated. Spread it on a baking sheet and roast in the oven for about 20 minutes, or until fork-tender, stirring halfway through.

While the squash is roasting, heat the remaining tablespoon of olive oil in a large skillet over medium-low heat. Add the sliced onions, sprinkle with a pinch of salt, and cook slowly for about 15 minutes, stirring occasionally, until they are soft and golden brown.

Once the onions are caramelized and the butternut squash is roasted, add the balsamic vinegar to the onions, stirring to combine. Then gently fold in the roasted squash. Adjust seasoning if necessary.

On a floured surface, roll out the sheet of puff pastry to fit into a tart pan or a baking dish. Place the pastry into the pan and trim the edges as needed.

Spoon the butternut squash and onion mixture onto the puff pastry base, spreading it out evenly. Top with grated cheese.

Bake in the preheated oven for about 20-25 minutes, or until the pastry is golden brown and puffed up.

Allow it to cool for a few minutes. Sprinkle with fresh thyme before slicing and serving.