Prepare Peach Syrup: In a medium saucepan, combine sliced ripe peaches, water, and granulated sugar. Bring to a rolling boil then simmer for 15 minutes. Allow to cool and strain the syrup.

Make Mascarpone Filling: Whip heavy cream until stiff peaks form. In another bowl, mix mascarpone cheese, sugar, the cooled peach syrup, vanilla extract, and almond extract until smooth. Fold in whipped cream.

Assemble Tiramisu: Briefly dip ladyfingers into peach syrup. Arrange half in a dish, spread half of the mascarpone filling, repeat with remaining ladyfingers and filling.

Chill: Cover and refrigerate for at least 6 hours, preferably overnight.

Serve: Slice into squares and garnish with fresh peach compote or leftover syrup.