Preheat your oven to 400°F (200°C).
In a food processor, combine the almond paste, granulated sugar, softened butter, egg white, and almond extract. Pulse until the mixture is smooth and spreadable. If you don't have a processor, mash the ingredients together in a bowl with a fork until uniform.
On a lightly floured surface, roll the puff pastry sheet out slightly to even it into a 10x12 inch rectangle.
Spread the almond filling down the center of the pastry in a long, narrow strip, leaving about an inch of space on all sides.
Fold the two long sides of the pastry toward the center, overlapping them slightly to fully enclose the filling, and pinch the seams to seal.
Carefully transfer the log to your parchment-lined baking sheet and bend it into an oval shape, joining the two ends together by tucking one inside the other and pinching to seal.
Bake for 25 to 30 minutes, or until the pastry is puffed and deep golden brown.
While the pastry cools, whisk the powdered sugar and milk together until smooth to create a thin glaze.
Drizzle the glaze over the warm kringle and immediately sprinkle with the sliced almonds.