Make the Dough:
In a large bowl, whisk flour and salt. Cut in cold butter until coarse crumbs form. Gradually add ice water, mixing until dough just comes together. Shape into a rectangle, wrap in plastic, and refrigerate for 2 hours or overnight.

Toast Almonds:
Preheat oven to 350°F. Spread slivered almonds on a baking sheet and toast for 8–10 minutes, stirring once, until golden. Cool and grind finely.

Prepare Almond Filling:
In a saucepan, combine sugar, cream, ground almonds, flour, almond extract, vanilla, and salt. Cook over medium heat, stirring constantly, until thickened and simmering (5–7 minutes). Cool completely.

Shape Kringles:
Preheat oven to 375°F. Line a baking sheet with parchment. Divide dough in half and roll each into a 12×18-inch rectangle. Spread almond filling evenly over each, leaving a 1/2-inch border. Roll jelly-roll style and form into horseshoe shapes. Place on baking sheet.

Bake:
Bake for 25–35 minutes, or until golden and internal temp is 200°F–210°F. Cool 10–15 minutes on the pan, then transfer to a wire rack.

Glaze and Serve:
Whisk powdered sugar, milk or cream, and almond extract until smooth. Drizzle over cooled kringles. Garnish with slivered almonds if desired. Let glaze set for 15–20 minutes before slicing.