Make 1 batch of my shortcrust pastry*. Make sure to omit the sugar and vanilla as this is a savory pastry. If your do not want to make your own crust, feel free to use 1 sheet of puff pastry.
Peel the onions and slice them into 3 to 4 thick rounds, like you would cut onion rings, but leave them together in a single round. This will create the beautiful circular patterns after baking.
Melt the butter over medium heat and add the olive oil. Once the butter is melted, add the sugar and salt and mix well until they dissolve. Next, add in your balsamic vinegar and mix. Finally, gently arrange the onion rounds in the bottom of the pan, trying to cover almost the entire pan. Simmer the onions on medium-low heat for 20 minutes.
While the onions are caramelizing, preheat your oven to 400°F. Additionally, roll out your shortcrust pastry or puff pastry a little larger than the size of your cast-iron pan. It should be about 12 inches round.
Once the onions are done, gently place your pastry over the top of your onions, and roughly tuck the pastry around. Be careful not to burn your fingers on the edges of your hot pan! Then cut a few small vent holes into your pastry to allow steam to escape, ensuring you do not have a soggy bottom.
Bake your tarte tatin for about 25 to 30 minutes, or until your pastry is nice and golden. Allow your tarte to cool for 5 minutes, then place a plate over the pan and invert to turn out the tarte. If some of the onions stick to the pan, that is ok! Just use a fork or tongs to remove and arrange back on the tarte.
Once your tarte is turned out, top it with your feta cheese and serve!
Storage Instructions: Store leftovers in an airtight container in the refrigerator for up to 4 days.
Reheating Instructions: Warm slices in the oven or air fryer at 350°F until heated through and the pastry is crisp again. Avoid microwaving, as it softens the crust.