In a large mixing bowl, combine the flour, sugar, salt, and yeast. Cut in the cold butter until the mixture resembles coarse crumbs. Gradually mix in the milk and beaten egg until a dough forms. Cover the bowl and chill in the refrigerator for at least 1 hour.

Meanwhile, prepare the filling by mixing the sliced apples with cinnamon, nutmeg, and sugar in a separate bowl. Toss until the apples are evenly coated and set aside.

After chilling, roll out the dough into a rectangle about 1/4 inch thick. Spoon the apple filling in the center, fold the dough over to create a horseshoe shape, and press the edges to seal.

Preheat the oven to 375°F (190°C). Transfer the shaped kringle to a parchment-lined baking sheet. Brush with the egg wash for a golden finish and bake for 25-30 minutes until golden brown and puffed.

Allow the kringle to cool for about 10 minutes. Whisk together the powdered sugar and vanilla extract, adding milk for desired consistency. Drizzle the glaze over the kringle.