Preheat your oven to 400°F (200°C) and line two large baking sheets with parchment paper. Keep the puff pastry refrigerated until ready to use.

In a medium bowl, beat the cream cheese with granulated sugar until smooth and fluffy, about 2 minutes. Mix in the egg yolk, vanilla extract, and almond extract until fully combined. Transfer to a piping bag or zip-top bag with one corner snipped off.

In a separate bowl, toss the diced peaches with cornstarch, brown sugar, and cinnamon until evenly coated. Set aside to let the juices mingle while you prep the pastry.

Unfold one sheet of puff pastry on a lightly floured surface and roll it gently to smooth any creases. Cut into 6 equal squares (about 3x3 inches each). Repeat with the second pastry sheet for 12 total squares.

Transfer the squares to your prepared baking sheets, spacing them 2 inches apart. Use a sharp knife to score a shallow border about 1/2 inch from the edges of each square, being careful not to cut all the way through. Dock the center area with a fork 8-10 times.

Pipe a generous layer of cream cheese filling into the center of each square, staying within the scored border. Top each with 2-3 tablespoons of the peach mixture, spreading it gently over the cream cheese.

Brush the exposed pastry edges with heavy cream, being careful not to let it drip onto the parchment. This creates the golden, crispy frame around your filling.

Bake for 18-22 minutes, rotating the pans halfway through, until the pastry is deeply golden and puffed around the edges. The centers should look set but still slightly soft.

While the Danish cool for 5 minutes, whisk together the powdered sugar, 2 tablespoons milk, and vanilla extract until smooth. Add the remaining tablespoon of milk if needed to reach a thick but drizzle-able consistency.

Drizzle the glaze over the warm Danish in a zigzag pattern. Let them cool for another 5 minutes before serving so the glaze sets into a glossy finish.