In a Boston shaker, lightly muddle basil leaves. You'd want to release the flavors but not to destroy the leaves.
Add Arrogante Blanco tequila, agave nectar and freshly squeezed juice of lemon. Stir well. Top the shaker off with a handful of ice cubes and shake vigorously for 15 to 20 seconds until the cocktail is well chilled.
Using a fine mesh strainer, strain the drink into a chilled cocktail glass. Drop in the glass two thin slices of lemon and garnish with a basil leaf. Serve with a straw.