Slice the fresh peaches and place them in a saucepan along with water and granulated sugar. Heat over medium-high until boiling, then simmer for about 15 minutes. Strain to separate syrup from peaches.

Allow the peach syrup and peach slices to cool completely in the refrigerator for at least 30 minutes.

In a mixing bowl, whip the heavy cream until stiff peaks form. In a separate bowl, combine mascarpone cheese, sugar, peach syrup, vanilla extract, and almond extract. Blend until smooth. Fold in whipped cream until light and airy.

Quickly soak each ladyfinger in the chilled peach syrup, layer in a dish, spoon half of the mascarpone filling over, and repeat with another layer.

Cover with plastic wrap and refrigerate for at least 6 hours or ideally overnight.

Slice into squares and serve chilled, possibly garnished with peach compote and leftover syrup.