Preheat your oven to 400℉. Wash and slice your peaches into ¼" thick slices.
Cut the puff pastry into nine equal squares and places them, slightly separated, on a baking sheet. Note: If the pastry squares are too small for the peach slices, you can slightly roll them out to be bigger, or dice the peach instead.
In a mixing bowl, combine the sugars, flour, cinnamon, and ¼ tsp vanilla until it's all well mixed. Stir in the peaches to coat them as well as possible.
Line 3-4 peach slices in the center of the pastry squares. Brush the edges with beaten egg. Sprinkle your almonds over the top.
Bake for 18 minutes, until the pastry is puffed and golden. About halfway in, rotate the baking sheet for more even baking.
Remove from the oven and let cool for around 15 minutes.
During this time, make your icing by combining the powdered sugar, milk, and remaining vanilla extract. Drizzle this over the slightly-warm pastries and enjoy!