Make the bread: Stir milk and sugar together in a small bowl. Sprinkle yeast over top and let stand for 10 minutes to dissolve. Stir in cream.
Stir together flour, sugar, salt, and cardamom in a separate bowl. Cut in butter with 2 knives or a pastry blender until texture is coarse and mealy. Add yeast mixture and stir until well blended. Pat into a ball, flatten slightly, and wrap in plastic wrap. Refrigerate for 12 to 24 hours.
When ready to bake, make the filling: Mix almond paste, almonds, sugar, cinnamon, and almond extract with an electric mixer in a large bowl until evenly blended. It may be crumbly.
Roll chilled dough into a 2x24-inch rectangle. Spread filling over dough to within 2 inches of each side. Roll up into a tube. Cover the work surface with sugar and roll dough tube into sugar until thoroughly coated.
Roll and stretch dough tube out into a 40-inch-long rope. Place onto a parchment-lined baking sheet and form into a pretzel shape.
Brush dough with egg white and sprinkle with almonds. Cover loosely with a towel and let rise for 45 minutes.
Preheat the oven to 375 degrees F (190 degrees C).
Bake kringle in the preheated oven until golden brown, 25 to 30 minutes. Cut into slices to serve.