In a large mixing bowl, combine all-purpose flour, salt, and sugar. Cut in chilled butter until the mixture resembles coarse crumbs. Gradually add cold water, mixing until the dough just comes together. Shape into a disk, wrap in plastic, and refrigerate for 30 minutes.

Prepare the apple filling by peeling and dicing apples. In a bowl, combine diced apples with brown sugar, cinnamon, lemon juice, and cornstarch. Let sit for 10 minutes.

Preheat your oven to 375°F (190°C). Roll out chilled dough into a rectangle about 1/4 inch thick. Transfer to a parchment-lined baking sheet. Spoon apple filling down the center, leaving 2 inches on each side for braiding. Make diagonal cuts along the sides.

Fold the flaps alternately over the apple filling to form a braid. Pinch ends to seal. Bake for 25-30 minutes until golden brown and fragrant.

In a medium bowl, whisk together powdered sugar, milk, and vanilla extract until smooth and pourable. Adjust consistency if necessary.

Slice into generous pieces to serve, best enjoyed warm alongside coffee or tea.