Make the Peach Syrup: Peel and chop the peaches. In a saucepan, combine peaches with water and sugar. Bring to a boil, then simmer for about 15 minutes until the peaches are soft and syrup thickens. Cool and strain to collect syrup.

Prepare the Mascarpone Filling: Whip heavy cream to stiff peaks. In another bowl, mix mascarpone, sugar, peach syrup, vanilla and almond extract until smooth. Fold in whipped cream gently in two stages.

Assemble the Tiramisu: Dip each ladyfinger in peach syrup for 2-3 seconds. Arrange half in an 8-inch dish, layer half the mascarpone filling, repeat with the rest.

Chill: Cover with plastic wrap and refrigerate for at least 6 hours or overnight for best results.

Serve: Cut into squares and serve with a drizzle of fresh peach syrup and reserved peach pieces if desired.