In a medium saucepan over medium heat, combine sliced peaches, water, and sugar. Bring to a boil, then reduce heat and simmer for 15 minutes until soft. Cool for 10 minutes and strain.

In a large bowl, whip heavy cream until stiff peaks form. In another bowl, mix mascarpone, sugar, peach syrup, vanilla, and almond extracts until smooth. Fold in whipped cream.

Dip ladyfingers in peach syrup briefly. Layer half in an 8-inch dish, spread half the mascarpone filling on top, repeat layers.

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

Slice chilled tiramisu and top each piece with reserved peach compote and remaining syrup before serving.