Peel and halve onions; melt half the butter and olive oil in a non-stick pan on low heat.
Place onions cut side down in the pan, drizzle with honey and balsamic vinegar, season with salt, cover, and cook for 7 minutes.
Flip onions, add remaining butter, cover, and cook for another 8 minutes on low heat.
Preheat oven to 400°F (200°C).
Arrange onions cut side down again, cover with puff pastry making two holes in the center, and bake for 15-20 minutes until golden.
Invert the tart onto a serving plate, optionally top with cheese sauce or grated cheese and melt in the oven for extra flavor.
Serve hot to enjoy the sweet and sour onion flavor with creamy cheese.
Quick Note
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Notes
I usually go for Gruyere because it melts so well and tastes amazing, but I don't hesitate to mix in other cheeses too. Mixing Gruyere with a bit of Parmesan brings in a nice, sharp edge that I love.
I've learned to bake the tart right in the middle of the oven. If I put it too low or too high, I either end up with a burnt bottom or an undercooked top that doesn't puff up right.
To avoid a soggy pastry, which nobody likes, I pre-bake the puff pastry for about 10 minutes before throwing on the toppings. It gives a sturdier base that doesn't get overwhelmed by the juicy onions and melting cheese.
The sweetness from the onions can be hit or miss, depending on how sweet they naturally are or how long I let them cook down. I keep tasting and tweak the amount of honey or vinegar I add to get it just right.