Prepare the apples: Wash, core, and thinly slice the apples using a mandoline slicer.
Soften the apples: Boil water with the juice of 1 lemon. Cook the apple slices in batches for about 50 seconds, until softened but not mushy. Remove with a slotted spoon and cool on paper towels.
Prepare the pastry: Thaw the puff pastry according to the package instructions. Gently stretch it out and spread a generous layer of apple butter over each sheet. Cut into strips wide enough to fit the muffin tin.
Make the roses: Arrange the apple slices along one side of each pastry strip, overlapping them slightly. Fold the pastry over the apples and gently roll each strip into a rose.
Bake: Preheat the oven to 385°F (195°C). Grease a muffin tin and place the apple roses inside. Brush with beaten egg and bake for about 45 minutes, or until golden and cooked through.
Make the syrup: Boil the water, sugar, and lemon juice together. Reduce the heat and simmer for about 8 minutes, then let it cool.
Finish: Brush the warm apple roses generously with the syrup. Carefully remove them from the muffin tin and cool on a wire rack before serving.
