Special equipment: a handheld blender, an ice cream maker
Combine the sugar, salt and basil with 1 cup water in a small saucepan and place over medium heat. Bring the mixture to a simmer, stirring occasionally to help dissolve the sugar. Simmer gently for 2 minutes. Using a slotted spoon, remove the basil from the simple syrup and discard. Whisk the egg white in a medium bowl until frothy. Whisk the hot syrup into the beaten egg white. Whisk in the lemon juice and olive oil. Switch to a rubber spatula and stir occasionally for 5 minutes or until just warm to the touch. Refrigerate until completely chilled, stirring occasionally, about 2 hours.
To freeze the sorbetto, use a handheld blender to emulsify the base mixture. When the base looks creamy and smooth, pour it directly into an ice cream maker and churn according to the manufacturer's directions, about 15 minutes. When the mixture is the consistency of a thick milkshake (do not overprocess or it will separate), transfer to an airtight container and freeze until ready to serve, at least 3 hours and up to overnight.
To serve, scoop the sorbetto into a small coupe or bowl, sprinkle with berries and drizzle with balsamic.