Preheat the oven to 400°F (200°C). Roll out the puff pastry and fit it into a pie dish. Prick the bottom with a fork and set aside.

In a skillet, heat olive oil over medium heat. Add sliced onions, salt, and sugar. Cook, stirring occasionally, until onions are golden brown and caramelized, about 25-30 minutes.

In a mixing bowl, whisk together the heavy cream, eggs, thyme, and a pinch of salt and pepper. Stir in the caramelized onions and grated cheese.

Pour the filling into the prepared pastry crust. Bake in the preheated oven for 25-30 minutes, or until the filling is set and the top is golden.

Allow the tart to cool slightly before slicing. Serve warm or at room temperature.