Heat the oven to 400 degrees. Line a baking sheet with parchment paper. Pulse the cottage cheese, cream cheese, sour cream, sugar, lemon peel, flour, 1 teaspoon lemon juice, and almond extract in a food processor until almost smooth.
On lightly floured surface, roll the puff pastry to a 14x12-inch rectangle and place on the parchment paper. Whisk the egg and water in a small cup. Spread the cottage cheese mixture lengthwise down the center of the pastry and top with the raspberries.
Cut 1-inch slits diagonally down both sides of the pastry to within 1/2-inch of the filling. Starting at the top, alternately fold the strips over to enclose the filling.
Lightly brush with the egg mixture and sprinkle with the coarse sugar. Bake for 30 to 35 minutes or until golden brown. Cool on a wire rack to room temperature.
Meanwhile, whisk the powdered sugar, milk, 1 teaspoon lemon juice, and corn syrup together (adding additional powdered sugar or milk if necessary to reach desired consistency). Drizzle the glaze over the pastry. Let stand until set.