Heat the oven to 400°F or 205°C. Line 6 cups of a standard 12-cup muffin tin with circles of parchment paper.

Bring a few cups of water to a boil, over the stove, or using an electric kettle.

Using a sharp knife or mandoline, thinly slice the apples around the core into half-moon slices 1 to 1½ millimeters thick. Soak the apples in boiled water for 3 to 5 minutes, until they become soft and bendable.

Roll the pastry to 2 millimeters thick. Cut lengthwise into 6 strips.

Arrange one-sixth of the apple slices on the top half of each strip, peel side up. Fold the pastry in half, over the apples, press down, leaving the rounded, unpeeled edges of the apple slices exposed at the top.

Roll up one apple-filled pastry strip, from one end, to the other, to form a rose. Cut the excess dough off if necessary and pinch the end of the dough strip to seal. Repeat with the remaining strips and set aside.

Add the sugar to a pan over medium-low heat. Allow the sugar to slowly melt in the pan, without stirring it. Cook undisturbed for about 10 minutes, until the sugar caramelizes to a deep amber.

Pour 2 to 3 soup spoons of caramel into each parchment paper lined muffin well. Arrange the apple roses upside down in each well, the apples should be touching the caramel.

Bake for 25 to 30 minutes, until the puff pastry is cooked through.

Allow the roses to rest for 5 minutes before serving. Carefully lift each rose, and remove the parchment paper to reveal the jammy apples.