Let's cook.
Preheat your oven to 400°F (200°C).
In a 9-inch oven-safe skillet (preferably cast iron), melt 1/2 cup unsalted butter over medium heat. Add 1 cup granulated sugar and cook, stirring occasionally, until the sugar dissolves and turns into a golden caramel, about 5-7 minutes. Be careful not to burn it.
Remove the skillet from the heat and carefully arrange the quartered apples tightly in a circular pattern over the caramel. Drizzle with 1/2 teaspoon vanilla extract.
Place the skillet back on medium-low heat and cook for 10-15 minutes, allowing the apples to soften slightly and absorb some of the caramel. This step helps prevent the apples from being too firm after baking.
Roll out the thawed puff pastry sheet slightly larger than your skillet. Carefully place the puff pastry over the apples, tucking the edges down around the apples and into the skillet.
Bake in the preheated oven for 25-30 minutes, or until the pastry is golden brown and puffed.
Remove the skillet from the oven and let it cool for 5-10 minutes. This cooling period is crucial for the caramel to set slightly, making inversion easier.
Place a large serving plate upside down over the skillet. Using oven mitts, carefully and confidently invert the tarte onto the plate. If any apples stick, gently place them back onto the tarte.
Serve warm, perhaps with a scoop of vanilla ice cream or a dollop of crème fraîche.
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