In a sturdy, thick-bottomed pint glass from a Boston shaker, use a bar muddler to crush the avocado, pineapple, cilantro leaves, and ginger into a fragrant, pulpy mush.
Pour in the vodka, lemon juice and agave syrup, swirling to combine.
Fill the metal part of the Boston shaker 2/3 full with ice.
Pour the muddled vodka mixture (including pulp) over the ice; cap the with the pint glass.
Shake vigorously until well chilled.
Using a Hawthorn strainer, double-strain the cocktail through a wire-mesh sieve into into an ice-filled double old-fashioned or highball glass. Garnish with lime wedge and cilantro sprig.