In a food processor, pulse flour, 1 tablespoon powdered sugar, yeast, and salt until combined.

Add cold butter and shortening; pulse until the mixture resembles coarse meal.

Transfer to a bowl and stir in sour cream and half of the beaten egg until a sticky dough forms.

Divide dough into two equal portions, wrap in plastic, and pat into 7x3-inch rectangles.

Refrigerate dough for at least 4 hours or overnight to allow the yeast to develop and the butter to chill.

In a medium bowl, mash almond paste with granulated sugar, egg white, and almond extract until a smooth spreadable paste forms.

On a floured surface, roll one dough portion into a 24x6-inch rectangle.

Spread half of the almond filling in a 2-inch wide strip down the center of the dough.

Fold the long sides over the filling, overlapping them slightly, and pinch the seam and ends tightly to seal.

Transfer to a parchment-lined baking sheet, shaping the log into an oval ring and tucking one end into the other.

Repeat the process for the second portion of dough and filling.

Preheat oven to 350°F (175°C) and bake for 20-25 minutes or until the pastry is light golden brown.

Whisk powdered sugar and milk together to create a smooth glaze.

Drizzle glaze over the warm kringles and immediately top with sliced toasted almonds.