Day 1: Make the dough. In a stand mixer, combine flour, sugar, yeast, and salt. Add warm milk, egg, and vanilla. Knead into a smooth, elastic dough. Shape into a square disc, wrap, and chill for 1+ hour.

Make the butter block. Pound cold butter between parchment into a 7x9-inch rectangle. Chill for 30 minutes.

Laminate. On a floured surface, roll dough to 10x15 inches. Place butter block in center. Fold dough flaps over butter and seal. Roll into an 8x20-inch rectangle. Perform a letter fold (fold into thirds). Wrap, mark '1', chill 45 min.

Repeat the rolling and letter folding process two more times, chilling for 45-60 minutes between each fold. After the third fold, wrap dough well and refrigerate overnight.

Day 2: Make the almond filling. Mix almond flour, sugar, egg white, softened butter, extracts, and salt into a thick paste. Add cream if too dry. Set aside.

Shape. Roll chilled dough into a 12x18-inch rectangle. Spread filling in a thick strip down the center third. Fold top third down, then bottom third up, sealing the seam to form a long log.

Transfer log to a parchment-lined baking sheet. Form into a large oval, overlapping and sealing the ends to create a wreath. Cover and let proof for 45-60 minutes until puffed. Preheat oven to 375°F (190°C).

Brush pastry with egg wash and sprinkle with sliced almonds. Bake for 25-30 minutes until deep golden brown. Cool completely on a wire rack.

Glaze. Whisk confectioners' sugar, 1 tbsp milk, and almond extract until smooth. Drizzle over cooled kringle. Let set before slicing.