Preheat the oven to 375°F (190°C). Line a baking sheet with parchment paper and set aside.

Prepare the almond filling by placing the butter, sugar, and almond paste into a food processor. Pulse until the mixture is smooth and fully combined. Add the egg whites and almond extract and process until a smooth paste forms. Add the flour and salt, mixing until a thick, cohesive filling is achieved. Set aside.

Arrange the puff pastry on the prepared baking sheet. Using the back of a knife, lightly mark the center section of the pastry lengthwise. Cut 45-degree diagonal strips approximately 2 inches apart along both sides of the marked center, leaving uncut flaps at the top and bottom ends.

Evenly spread the almond filling down the center of the pastry, leaving a 2-inch border at the ends. Spoon the cherry pie filling over the almond layer, focusing on the cherries and minimizing excess gel to prevent leakage.

Fold the top and bottom pastry flaps over the filling. Braid the pastry by alternately folding the diagonal strips over the filling, overlapping slightly, until fully enclosed.

Whisk together the egg yolks and 1 tablespoon of water to create an egg wash. Brush the entire pastry evenly with the egg wash. Sprinkle the toasted sliced almonds over the top.

Bake for 22 to 25 minutes, or until the pastry is puffed and golden brown.

While the Danish bakes, prepare the glaze by whisking together the powdered sugar, almond extract, vanilla extract, and heavy cream until smooth. If using the apricot glaze, warm the jam with 2 tablespoons of water and stir until thinned.

Remove the Danish from the oven and immediately brush with the warm apricot glaze, if using. Drizzle or spread the almond glaze over the warm pastry. Allow to cool slightly until the glaze sets before slicing and serving.