Peel, quarter and core the apples
Pre-heat the oven to 375F (or 350F in convection oven)
In a cast iron pan or oven proof pan, add the butter in chunks and sprinkle the sugar.
Add the apple by placing a half in the middle like a button and the remaining slices flat side down in a concentric circle like flower petals making sure they are close together.
Turn the heat on medium and cook for 3-5 minutes making sure to flip the slices once or twice so that they caramelize evenly.
The apples will produce extra bubbling liquid you can remove with a spoon or a baster.
The key is to start on medium heat and keep cooking the apple and sugar until the juice evaporate and get darker and thicker. You will smell the caramel when it is ready. This shouldn't take more than 10 minutes depending on your stove. Remove from heat.
Measure the diameter of your pan. Roll out the thawed puff pastry and cut a circle a little larger than your pan.
Lift the dough and place on top of the hot apples. Gently tuck the edges and push down onto the apples.
Place in the oven and bake for 45-40 minutes until the top is brown and crispy.
Let it cool down 3-5 minutes. Using a larger plate, flip the tart using oven mitts.
Cut slices and serve warm as is or with your favorite vanilla ice cream.