In a shaker, muddle strawberries and basil. Fill shaker three-fourths full with ice. Add the remaining ingredients; cover and shake 10-15 seconds or until condensation forms on outside of shaker. Strain into a chilled cocktail glass.
To make your own simple syrup: In a small saucepan, combine 2 cups sugar and 1 cup water; bring to a boil over medium heat, stirring to dissolve sugar. Reduce heat; simmer 3 minutes, stirring occasionally. Cool completely. Store, covered, in refrigerator for up to 2 weeks. Use to sweeten cocktails, iced tea or lemonade. Yield: 1-2/3 cups.