In a small bowl, combine sugar, salt and grated ginger. Mixture will be moist, so spread into a thin layer on a plate or baking sheet and leave out to dry for about 1 hour or overnight.
Place agave syrup and sliced ginger into a small saucepan. Bring to a boil over medium heat, then simmer for about 5 minutes. Remove from heat and let cool completely. Discard ginger.
Run a lime wedge around glasses. Dip each glass into salted ginger sugar and set aside. Add tequila, Cointreau, lime juice, ginger syrup, tamarind paste and ice to a blender. Blend until slushy. Add more ice if necessary. Pour immediately into glasses. Garnish with lime wedges.