In a saucepan over medium heat, combine chopped fresh peaches, water, and granulated sugar. Bring to a boil, then simmer for about 15 minutes. Cool and strain.

In a mixing bowl, whip heavy cream until stiff peaks form. In another bowl, combine mascarpone cheese, sugar, peach syrup, vanilla extract, and almond extract. Fold the whipped cream into the mascarpone mixture.

Dip savoiardi ladyfingers into chilled peach syrup and line them in an 8-inch dish. Spread half of the mascarpone filling, add another layer of ladyfingers, and top with the rest of the filling.

Cover and chill in the refrigerator for at least 6 hours, preferably overnight.

Serve chilled with a drizzle of peach syrup.