To start off, activate your yeast by combining the warm milk and water with the active dry yeast. Let it sit for about 5 minutes until foamy.
In a large mixing bowl, whisk together the all-purpose flour, kosher salt, and granulated sugar. Cut in the cold cubed butter until it resembles coarse crumbs.
Add the foamy yeast mixture and an egg to the flour mixture. Stir gently until just combined, then form the dough into a ball, wrap it in plastic wrap, and refrigerate for at least an hour.
Preheat your oven to 375°F (190°C). On a floured surface, roll out your dough into a large rectangle.
Spread the apple pie filling down the center of the rolled-out dough and sprinkle with ground cardamom. Fold the dough over the filling and shape it before transferring to a baking sheet.
Brush the kringle with an egg wash if desired and bake for about 22-25 minutes until flaky and golden. Let it cool completely on a wire rack.
Mix powdered sugar with vanilla extract and enough water to achieve a smooth consistency. Drizzle over the cooled kringle and allow it to set before slicing.