In a medium saucepan over medium heat, combine diced peaches, water, and granulated sugar. Bring to a gentle boil, then simmer for 15 minutes. Strain syrup and let cool.

Whip heavy cream until stiff peaks form. In another bowl, blend mascarpone cheese, granulated sugar, cooled peach syrup, vanilla extract, and almond extract until smooth. Fold in whipped cream.

Dip each ladyfinger into cooled peach syrup for 2 seconds on each side. Layer half of the soaked ladyfingers in a dish, followed by half of the mascarpone filling. Repeat with remaining ingredients.

Cover with plastic wrap and chill in the refrigerator for at least 6 hours or overnight.

Slice and serve chilled. Drizzle with additional peach syrup and fresh peach compote if desired.