In a saucepan, combine sliced peaches, water, and granulated sugar. Bring to a boil over medium heat, then simmer for about 15 minutes until thickened.

Remove from heat, cool, and strain to reserve the syrup.

Whip heavy cream until stiff peaks form. In another bowl, mix mascarpone, sugar, peach syrup, vanilla and almond extracts until smooth. Fold whipped cream into the mascarpone mixture.

Dip ladyfingers quickly into the peach syrup and arrange in a square dish. Spread half of the filling over the ladyfingers and repeat with another layer.

Cover and refrigerate for at least 6 hours or overnight.

Slice and serve, optionally garnished with peach compote and extra syrup.