Granita, which means "water ice" in Italian, is a coarsely textured frozen dessert made with fresh fruit or juice. For an easy, no-hassle summer treat that doesn't require an ice cream maker, it can't be beat. Combine a few simple ingredients and freeze them together in a shallow pan, stirring the mixture a few times while it hardens. The resulting ice crystals are scraped with a fork to create a fluffy slush, similar to snow cones in texture. The granita will keep up to 3 days in the freezer.
Place the all but 3 of the apricots in the bowl of a food processor; reserve the 3 apricots for garnish. Add the sugar, water, lemon juice, salt, almond extract, and apricot brandy, if using, to the food processor. Purée until the mixture is smooth. If a few bits of apricot remain, that's okay; they will add texture to the granita.
Transfer the mixture to an 8- or 9-inch square baking pan and cover with plastic wrap. Freeze for 1-1/2 hours. Stir the mixture with a fork, breaking up the crust that will have formed and mixing well. Return the ice to the freezer and stir again every 45 minutes, smoothing the top after stirring, until the granita is completely frozen.
Just before serving, cut the reserved 3 apricots into quarters. Whip the cream to soft peaks. To serve, scrape the granita with a fork, creating fluffy ice crystals. Divide the granita among clear glass bowls or glasses and garnish each serving with a dollop of whipped cream. Top with slices of fresh apricot and serve immediately.