Honeydew melons are very juicy but they can lack flavor unless perfectly ripe. The one I got my hand on was in a pretty nice ripeness stage but, still, honeydews aren't typically bursting with flavor. That's where flavored vodkas and liqueurs come into play.
With the addition of a little honey for added sweetness and some lemon juice this turned out to be a very pleasant and refreshing cocktail for a warm (read that hot, I'm in Arizona) late summer evening.
The Honeydew Melon Martini
2 Oz. Melon Vodka
1/2 Oz. Midori
1 Oz. Honeydew Melon Puree
Juice of 1/2 Lemon
1 Tbsp. Honey
1 Oz. Sparkling Wine or Soda
Slice of Honeydew for Garnish
Puree small chunks of honeydew in a blender or food processor. Chill your glass in the freezer. Combine the melon vodka, Midori, Honeydew puree, lemon juice and honey in a cocktail shaker with ice and shake until well blended and chilled. Pour into your glass, top off with the ounce of sparkling wine or soda and garnish with a slice of honeydew.