Preheat oven to 400 degrees F. Lightly spray a 12-cup muffin tin with non-stick cooking spray.

In a large bowl, combine sugar, cinnamon, cardamom, and allspice. Add apple slices and toss to coat.

Does a clean work surface with flour. Unfold the thawed, cold puff pastry and roll it out to a 10-inch square. Cut into 1-inch strips and set aside. Dust the surface again; roll almond paste into a 5-by-8-inch rectangle. Cut into 10 strips (¹⁄₂-inch by 8-inches).

Top each pastry strip with an almond paste strip and layer on apples lengthwise, leaving a 1-inch gap at each end. Starting at a short edge, tightly roll up the pastry into a coil. Place in the prepared muffin tin. Place the tin in the freezer for 5 minutes.

Bake the tarts until golden brown, 20 to 25 minutes.

*Recommended apples for baking are Granny Smith, Honeycrisp, Crispin, Braeburn, or Pink Lady. A mandoline or hand-held slicer is best for producing thin slices. Otherwise, carefully use a wide vegetable peeler.