Heat the oil and butter in a large skillet over medium-low heat. Add the onions with a big pinch of salt and stir. Cook, stirring often, until the onions become caramely, about 25 to 30 minutes. Be sure to watch carefully and lower the heat as needed so the onions don’t burn. I usually caramelize mine over low heat. They don’t need to be fully caramelized since they will also cook in the oven a bit!
Preheat the oven to 425 degrees F. Line a baking sheet with parchment paper. Place the sheet of puff pastry on the parchment paper. (Note: I did a fancy twist of puff pastry on the edges of mine, I just used the second sheet of puff pastry and cut it into strips, then twisted them. This is not necessary!)
Place the caramelized onions all over the sheet of puff pastry. Add the brie cheese slices on next. Then cover with the apple slices. Sprinkle on a pinch of salt and pepper if you’d like. Brush the exposed edges of the pastry crust with the egg wash.
Bake for 2o to 25 minutes, or until the pastry is golden and puffed. Remove and sprinkle with the pomegranate arils. Drizzle with the pomegranate molasses. Slice and serve!
This is best served warm. It’s okay at room temperature too! To reheat leftovers, I’d suggest warming them in a low oven for a few minutes. But it is best served right away.