Heat a saucepan over medium-high heat and combine peaches, water, and granulated sugar. Bring to a boil, reduce heat, and simmer for 15 minutes until it thickens and peaches soften. Cool, strain, and chill syrup and peaches.

In a mixing bowl, whip heavy cream to stiff peaks. In a stand mixer, mix mascarpone, sugar, peach syrup, vanilla, and almond extract until smooth. Gently fold in whipped cream.

Dip ladyfingers in chilled peach syrup for 1-2 seconds and lay in an 8-inch square dish. Spread half of mascarpone filling over ladyfingers. Repeat with another layer of ladyfingers and remaining filling.

Cover with plastic wrap and refrigerate for at least 6 hours. Serve chilled, optionally topped with peach compote or peach syrup.