Cream butter and 2/3 cup flour in a medium bowl until well combined. Divide into 2 equal parts, then roll each half between 2 pieces waxed paper into a 6x12-inch sheet. Chill butter sheets in the refrigerator.

Mix 3 cups flour with active dry yeast in a mixing bowl; set aside.

Stir together milk, sugar, and salt in a small saucepan over medium heat. Heat until warm, but not hot to the touch, about 115 degrees F (43 degrees C).

Pour warm milk mixture over flour mixture. Add eggs, lemon extract, and almond extract. Stir for 3 minutes. Knead in remaining flour, 1/2 cup at a time, until dough is firm and pliable. Cover and let rise at room temperature until doubled in size, 30 minutes to 1 hour.

Cut dough in half. Roll each half out to a 14-inch square. Place one cold butter sheet over half of each dough square, off to one side, then fold dough over butter sheet like the cover of a book. Pinch the edges of dough together with your fingers.

Roll each piece out to a 20x12-inch rectangle. Fold into thirds like a letter. Repeat rolling and folding one more time. Wrap in plastic and refrigerate for at least 30 minutes.

Roll and fold each piece of dough two more times. Wrap in plastic and refrigerate for at least 30 minutes.

Roll dough out to 1/4-inch thickness. Cut dough into squares. Place a dollop of fruit preserves in the center. Fold 2 opposite corners over the center to form a filled diamond shape. Place danishes on an ungreased baking sheet. Allow to rise at room temperature until doubled in size, about 30 minutes.

Preheat the oven to 450 degrees F (220 degrees C).

Brush beaten egg white over pastries.

Bake in the preheated oven until the bottoms are golden brown, 8 to 10 minutes.