01 - Preheat the oven to 400°F. Line a baking sheet with parchment paper.
02 - In a skillet over medium heat, melt the butter. Add diced apples, brown sugar, cinnamon, and salt. Cook, stirring regularly, for 5 to 7 minutes until the apples are soft and caramelized. Remove from heat and allow to cool.
03 - On a lightly floured surface, roll out the puff pastry to smooth any creases. Using a 3-inch round cutter, cut out 16 circles. Use a smaller cutter to create a center hole in 8 of the circles.
04 - Spoon a small amount of caramelized apple filling onto each of the 8 uncut circles of puff pastry. Cover with the 8 pastry rings, gently pressing to seal the edges.
05 - Brush the top of each assembled pastry donut with beaten egg to encourage browning and crisp texture.
06 - Transfer the assembled donuts to the prepared baking sheet. Bake for 18 to 20 minutes, or until golden brown and puffed.
07 - While the donuts bake, in a small saucepan over medium heat, melt sugar and butter until amber and bubbling. Remove from heat, carefully whisk in heavy cream and salt until smooth. Allow to cool briefly.
08 - Drizzle the cooled caramel glaze generously over the warm donuts before serving.