Prepare the pulp of the mango into a puree. Half fill the bottom of the shaker with crushed ice, add sugar, juice of one lemon, mango syrup (a little less if you like), vanilla, a little grated lime peel. Shake well.
Pour the mango puree into a chilled glass form, pour the mixture from the blender through the bar strainer on top. Blend again and add a few ice cubes.
Bring to the table garnished with a slice of lime and a straw.