In a medium saucepan, combine diced peaches, water, and granulated sugar over medium heat. Bring to a gentle boil and simmer for 15 minutes. Remove from heat, cool, and strain.

While syrup cools, slice peaches and chill in the refrigerator along with syrup.

Whip heavy cream until stiff peaks form. In another bowl, combine mascarpone, sugar, peach syrup, vanilla, and almond extract. Mix and fold in whipped cream.

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

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

Slice and serve chilled with a dollop of peach compote or remaining syrup.