In a medium saucepan, combine sliced peaches, water, and granulated sugar. Bring to a boil, then simmer for 15 minutes until peaches are tender. Remove from heat and strain the liquid, chill in the refrigerator.

Whip heavy cream in a large mixing bowl until stiff peaks form. In another bowl, mix mascarpone cheese, chilled peach syrup, vanilla extract, and almond extract until smooth. Fold whipped cream into mascarpone mixture.

Quickly dip ladyfingers in chilled peach syrup and lay half in an 8-inch square dish. Spread half the mascarpone filling over this layer, then top with another layer of soaked ladyfingers and remaining mascarpone filling.

Cover and refrigerate for at least 6 hours, ideally overnight to allow flavors to meld.

When ready to serve, slice into squares and garnish with reserved peach compote and leftover syrup.