Preheat the oven to 375 degrees F. Grease a 12 cup muffin tin.
Slice apples with a mandoline (or sharp knife) to paper-thin slices
Sauté apple slices in 2 teaspoons water over low-medium heat until the apples just start to soften, roughly 30 seconds per side.
Mix together butter, apricot preserves, sugar and cinnamon in a small bowl and microwave for 20 seconds then whisk to combine
Roll puff pastry sheet to less than 1/8-inch thickness into two rectangular shapes of about 12 x 9 inch each. Cut each square into 6 strips (roughly 2 x 9 inches).
Spread melted butter mixture over dough with a pastry brush then place apple slices along one long side of dough, about 1/2 inch beyond the edge, overlapping slices by about 1/4 inch. Fold the bottom half of dough up in half over apple slices.
Starting at one end, roll the dough to form a rose-shaped pastry making sure to keep the apple slices in place. Seal roll with end of dough strip.
Beat together eggs in a small bowl and bush surface of dough using a pastry brush then sprinkle with additional sugar and transfer roses to the greased muffin pan.
Bake on the middle rack in the preheated oven for 30 minutes then cover loosely with aluminum foil and bake another 15 minutes until pastry dough is fully cooked.
Remove from oven and allow to cool for 5 minutes. Remove apple roses from the muffin cups and finish cooling on a wire rack. Dust with powdered sugar before serving.