In a large bowl, combine the flour and cubed butter. Using a pastry cutter or your fingertips, work the butter into the flour until it resembles coarse crumbs. Stir in the sour cream until a shaggy dough forms. Divide it into two equal portions, flatten into discs, wrap in plastic wrap, and refrigerate for at least 4 hours or overnight.

In a saucepan over medium heat, combine the diced apples, brown sugar, cinnamon, flour, and lemon juice. Cook for about 5–7 minutes until the apples soften slightly and the mixture thickens. Let it cool completely.

On a lightly floured surface, roll out one disc of dough into a 10×6 inch rectangle. Spoon half of the apple filling down the center lengthwise. Fold both sides over the filling, overlapping slightly, and seal the edges. Gently shape it into an oval or horseshoe. Repeat with the second disc of dough and the remaining filling.

Preheat your oven to 375°F (190°C). Place the kringles on a parchment-lined baking sheet. Bake for 25–30 minutes or until golden brown. Let them cool slightly before glazing.

Whisk together the powdered sugar, milk, and vanilla until smooth. Drizzle generously over the cooled kringles. Let set before slicing.