01 - Preheat oven to 400°F (200°C).
02 - In a 9-inch ovenproof skillet or tarte Tatin pan, melt 1/2 cup sugar over medium heat without stirring until it reaches a deep amber color. Gently swirl the pan to distribute the color evenly.
03 - Add 1/4 cup unsalted butter, 1 teaspoon vanilla extract, pinch of salt, and 1/2 teaspoon cinnamon if desired, stirring until smooth.
04 - Place apple quarters in the pan, cut side up, packing them tightly. Cook over medium heat for 12 to 15 minutes, basting occasionally with caramel, until apples begin to soften and caramel thickens. Remove from heat.
05 - Roll out puff pastry to slightly larger than the pan diameter. Drape pastry over the apples, tucking the edges down around the fruit.
06 - Bake in preheated oven for 25 to 30 minutes, until the pastry is golden and crisp.
07 - While the tart bakes, line a baking sheet with parchment paper. In a small saucepan over medium heat, combine 1/3 cup sugar and 1 tablespoon water. Do not stir. Cook until it turns golden amber. Stir in 1/4 teaspoon sea salt and crushed candies, then quickly pour mixture onto the prepared sheet. Let cool, then break into small shards.
08 - Cool tart for 5 minutes, then carefully invert onto a serving plate while still warm.
09 - Before serving, sprinkle candy crunch shards over the tart for added sweetness and texture.