In a small bowl, combine active dry yeast, 3 tablespoons of granulated sugar, and 4 teaspoons of water. Let sit for 5-10 minutes until foamy.

In a large bowl, whisk together all-purpose flour and kosher salt.

Cut the cold, cubed butter into the flour mixture using a pastry blender, two forks, or fingertips until it resembles coarse crumbs with pea-sized pieces.

Pour the foamy yeast mixture and whole milk into the flour and butter bowl. Mix until a shaggy dough forms.

Turn the dough onto a lightly floured surface and knead for 5-7 minutes until smooth and elastic.

Lightly oil a clean bowl. Place the dough in the bowl, turning to coat. Cover with a kitchen towel or plastic wrap and let rise in a warm spot for 1 to 1.5 hours, or until doubled in size.

Punch down the dough and turn it onto a lightly floured surface. Roll into a 10x14 inch rectangle.

Spread apple pie filling evenly over the dough, leaving a 1-inch border on one long side. Sprinkle with ground cardamom.

Starting from the opposite side of the border, tightly roll up the dough like a jelly roll. Pinch the seam to seal.

Gently curve the rolled dough into a horseshoe shape and place on a baking sheet lined with parchment paper.

Cover the kringle loosely and let it rise for another 30 minutes.

Preheat oven to 375°F (190°C).

In a small bowl, whisk together the egg and 1 tablespoon of water. Brush the egg wash over the kringle.

Bake for 20-25 minutes, or until golden brown.

While the kringle bakes, whisk together powdered sugar and vanilla extract in a small bowl. Add milk, 1 teaspoon at a time, until a smooth, drizzle-able consistency is reached.

Let the kringle cool on the baking sheet for a few minutes, then transfer to a wire rack to cool slightly.

Drizzle the vanilla glaze over the warm kringle.