Preheat the oven to 400°F (200°C) and line a baking sheet with parchment paper. Unfold the thawed puff pastry sheet onto a lightly floured surface. Gently smooth over the fold lines with a rolling pin without rolling it thinner. Cut the sheet into 6 even squares using a sharp knife or pizza cutter.
In a mixing bowl, beat the softened cream cheese with a hand mixer or sturdy whisk until smooth. Add the granulated sugar and vanilla extract and mix until fully combined and lump-free. Set aside at room temperature.
In a separate bowl, toss the sliced peaches with the brown sugar, ground cinnamon, and cornstarch. Stir gently until every slice is coated and no dry cornstarch remains. Let sit for 5 minutes to allow the sugar to draw out juice.
Place the puff pastry squares on the prepared baking sheet, spaced at least 2 inches (5cm) apart. Score a smaller square about 1/2 inch (1.3cm) from the edge of each pastry square, cutting only halfway through the dough. Spread about 1 tablespoon of the cream cheese filling inside the scored border, then arrange 4 to 5 peach slices on top in a fan pattern.
In a small bowl, whisk the egg with the tablespoon of water to make the egg wash. Brush the egg wash only over the outer border of each pastry square, avoiding the filling.
Bake for 18 to 20 minutes, or until the pastry border is puffed and golden brown and the peaches look slightly caramelized at the edges. Rotate the baking sheet halfway through if your oven browns unevenly.
Remove from the oven and let cool on the tray for 5 minutes. Transfer to a wire cooling rack to cool for another 10 minutes before glazing.
In a small bowl, whisk together the powdered sugar, 1 tablespoon of heavy cream, and vanilla extract. Add the second tablespoon of cream only if the glaze is too thick to drizzle easily. Drizzle the glaze over the cooled danishes and sprinkle with sliced almonds immediately.