Make the simple syrup:
Bring the water to a boil. Add the sugars and whisk until dissolved. Add the basil and steep for 30 minutes. Discard the basil leaves and refrigerate the simple syrup until ready to use.
To make a Paloma:
Add the fresh lime juice, simple syrup and mezcal or tequila to a cocktail glass.
Fill with crushed ice.
Add the grapefruit soda and club soda. Stir to mix well.
Garnish with fresh basil leaves and a grapefruit slice.