Peel and core the pineapple, then cut half of the pineapple into chunks (reserve remaining half for another use).
Puree with basil in a food processor smooth and foamy (about 1 minute).
Combine 1/2 cup pureed pineapple with lemon and lime juices and sugar.
Strain the juice mixture into a pitcher and add tequila, Triple Sec, and remaining crushed ice.
Stir until well combined (about 1 minute).
Divide 1 cup of crushed ice between 4-6 margarita glasses.
Strain into ice-filled glasses to serve.