Cucumber Margaritas

• 3 cups peeled, seeded, and thinly sliced cucumbers (from 1 pound of cucumbers)
• 1 1/2 cups 100-percent agave silver tequila, preferably Milagro or Cazadores
• 1 cup fresh lime juice
• 1 cup simple syrup
• 1 lime half for moistening the glass rims
• Coarse kosher salt
• 6 to 7 cups ice cubes (preferably on the small side)
• Cucumber slices for garnish

Make the base: in a blender, combine the cucumbers, tequila, lime juice, and simple syrup. Blend until the mixture is as smooth as you can get it. Strain into a pitcher, cover, and refrigerate until chilled, about 1 hour.  

Moisten the rims of three 6-ounce martini glasses with the lime half. Spread the salt on a small plate, then upend the glasses into the salt to crust the rims. Fill a cocktail shaker three quarters of the way full with ice, then add 1 1/2 cups of the chilled margarita base. Cover and shake for 10 to 15 seconds. Strain into the prepared glasses. Garnish with cucumber slices. Repeat to serve 2 more rounds of 3 margaritas.