1. Cut the pineapple in half crosswise; reserve half, place in a resealable food storage bag and refrigerate.

2. Cut the remaining half into cubes and place them in a food processor. Purée until smooth. Measure 1 1/2 cups and refrigerate, reserving any excess for another use.

3. Combine the water and sugar in a small saucepan over high heat. Bring to a boil to form a syrup and cook for 3 minutes, stirring to make sure the sugar has dissolved. Transfer the syrup to a container and cool to room temperature (either in the refrigerator or on the counter), then combine with the reserved 1 1/2 cups pineapple purée and the salt. Cover and refrigerate until well chilled (at least 1 hour or up to 4 hours).

4. Process in an ice cream maker according to the manufacturer's directions; transfer to a tightly sealed container and freeze for at least 45 minutes and up to 4 hours (the sorbetto may not be quite firm).

5. When ready to serve, slice the remaining pineapple half into the thinnest possible rounds. Divide the slices among individual plates. Sift the confectioners' sugar through a fine-mesh strainer across the slices. Place 2 scoops of sorbetto on each plate. Garnish with mint leaves and serve immediately.

Adapted from Faith Heller Willinger's Adventures of an Italian Food Lover.