If desired, rim a glass with coarse sugar or salt. Run a lime wedge around the edge and dip the glass in your chosen rimming ingredient.
In a cocktail shaker, combine tequila, limoncello, triple sec, lime juice, and strawberry puree with ice.
Shake vigorously for 15-20 seconds until well chilled.
Strain into the prepared glass over fresh ice.
Garnish with a slice of lime and a fresh strawberry. Serve immediately.