Put water and sugar in a medium saucepan over a medium heat and stir until sugar dissolves. Bring to a simmer.
Cut 1 apple into quarters, then cut out core being careful not to break the apple. Using a mandolin, thinly slice apple quarters, then drop slices into sugar syrup and simmer for 4-5 minutes or until tender. Lift apple slices out of saucepan using a mesh spoon to drain, then place on a plate. Repeat with remaining apples. Simmer remaining syrup for about 3 minutes or until thickened, then set aside.
Preheat oven to 180°C. Grease a 24-hole non-stick mini muffin tin. Combine extra sugar and cinnamon in a small bowl. Brush 1 sheet of pastry with egg and sprinkle a thin layer of cinnamon sugar over top.
Cut out 16 pieces of pastry using a 6cm flower or round pastry cutter. Press pastry pieces gently into holes of prepared tin. Lay 4 to 5 slices of apple in a line, overlapping each other, then roll up to form rose. Hold to secure shape and place inside pastry cases.
Bake for 15 minutes or until golden. Cool in tin for 5 minutes before transferring to a wire rack to cool. Brush each tart with remaining sugar syrup. Re-grease tin and repeat steps 3 to 5 to make more tarts. Serve.