Combine sour cream and vanilla in a small bowl and set aside.

Cut flour and chilled butter using a pastry blender until it resembles small peas.

Stir in the sour cream mixture and blend well to form a dough.

Shape the dough into a disk, flatten slightly, cover, and chill for at least 2 hours or overnight.

Prepare the kringle filling while the pastry is chilling.

In a small saucepan, brown butter over medium heat, swirling occasionally.

Add diced apples, sugar, cinnamon, and vanilla to the browned butter.

Cook until apples have softened.

Whisk in cornstarch and cook until the mixture thickens, about 5 minutes.

Remove from heat and transfer the filling to a bowl.

Cover and refrigerate the filling until completely chilled, about 2 hours.

Move the oven rack to the center position and preheat the oven to 450°F.

Whisk together egg and sugar in a small bowl for the egg wash and set aside.

On a floured work surface, roll out the dough disk into a 12x6 inch rectangle.

Spread the chilled filling down the center in a thin strip, leaving 2 inches clear on each side and 1.5 inches at both ends.

Fold the sides over the center, then fold the ends up, and press lightly to seal.

Brush with the egg wash.

Bake on a parchment-lined cookie sheet for 10-15 minutes or until golden brown.

Just before the kringle finishes baking, whisk together powdered sugar, milk, and vanilla in a small bowl for the icing.

Drizzle the icing over the warm kringle.

Cool on a wire rack.

Store in a covered container. Best within a day.