Lay the apple on its side and slice into ½ inch (1.25cm) thick rounds. Use a small circular cutter to punch out the core and seeds from each ring.
Whisk together the lemon juice, brown sugar, and pumpkin spice. Add the apple rings and coat thoroughly.
Divide the thawed pastry sheet into 4 equal squares. Cut 90° angled slits into each corner of the squares.
Place an apple ring in the center of each square, then fold the pastry corners inward over the apple, pressing gently to adhere and form a ribbon pattern.
Brush the exposed pastry with beaten egg. Spoon a little of the remaining spiced syrup into the center of each pastry.
Bake at 400°F (200°C) until puffed and golden, about 20 minutes.