Break the ladyfingers into pieces and place in a food processor with the sugar. Pulse until the cookies form fine crumbs. Add the almond flour and salt and pulse to combine. Drizzle in the butter and pulse a few seconds, until the mixture sticks together when you pinch it between your fingers.

Transfer the dough to an 8-inch tart pan with a removable bottom, and press it evenly across the bottom and up the sides. Put the pan in the refrigerator to chill while you make the filling.

Put the cream cheese, crème fraiche, sugar and extract into the food processor and process until smooth and creamy, about 1 minute.

Scrape the filling into the tart pan, smoothing the top. Cover with plastic wrap and chill in the refrigerator for at least 4 hours or overnight.

In a medium bowl, whisk the sugar with ¼ cup water. Stir in the prosecco until sugar is completely dissolved (the prosecco will foam) Slice the peaches into ½-inch wedges and add to the bowl. Gently stir the peaches to coat with syrup. Cover and chill in the refrigerator until very cold, about 2 hours.

When ready to serve the tart, carefully separate the tart base from the sides by pushing upward. Put the tart on a serving plate.

Use a slotted spoon to lift the fruit from the syrup and arrange over the top of the tart. Slice and drizzle a little syrup over each serving.