Pesche alla Nonna
Michael's notes: You'll have an easier time pitting the peaches if you buy a freestone variety, but clingstone peaches will work. Don't[ peel the peaches ahead of time; they deteriorate quickly.]
Combine the water, vanilla bean, salt, lemon juice, and sugar in a large saucepan. Bring to a simmer over moderate heat, stirring to dissolve the sugar.
Peel the peaches with a vegetable peeler and leave whole. Add the peaches to the simmering liquid, cover, and adjust the heat to maintain a gentle simmer. Poach the peaches until they are barely tender when pierced with a knife, about 4 minutes; they will continue to cook as they cool. Remove them from the poaching liquid with a slotted spoon; reserve the syrup. When they are cool, halve the peaches and remove the pits.
Strain the syrup, let cool thoroughly, then pour it over the peach halves. Cover and chill the peaches.
Put the raspberries in a blender with 1/2 cup of the syrup from the chilled peaches. Blend until smooth, then strain through a fine-mesh sieve to remove the seeds. Thin the raspberry sauce, if needed, with a little more syrup. Taste and add a little superfine sugar if the sauce needs sweetening.
To serve, cut each peach half into 3 slices. Make a pool of the raspberry sauce on 6 dessert plates. Put a scoop of ice cream in the center. Surround with the peach slices. Crumble an amaretti cookie over the top and serve.