Special equipment: an immersion blender; 4 sets of chopsticks
Cut a thin slice off one long side of the watermelon so you can stand it securely on a cutting board. Trim off about the top one-sixth of the watermelon on the opposite long side. Transfer the watermelon to a baking dish or roasting pan (to catch the juice). Carefully press an immersion blender into the flesh of the watermelon and turn on low. Puree the flesh, being careful to keep the head of the immersion blender always immersed in the juice to avoid splattering. Remove and strain the juice.
Pour 8 cups of the strained juice back into the watermelon, then pour the rest into an ice cube tray and freeze for serving. Mix the vodka and lime juice into the watermelon. Cover the watermelon with plastic wrap and chill until cold, about 2 hours.
To make the kiwi shot glasses, trim off both rounded ends of the kiwis and carefully peel off the skin using a sharp paring knife. Cut each kiwi in half and carve out the seedy centers with the paring knife, being careful not to cut all the way through. Cover with plastic wrap and refrigerate until ready to serve.
Transfer the watermelon to the table. Arrange 4 sets of chopsticks over the top in pairs about 1 inch apart. Arrange the kiwi shot glasses so that 2 kiwi halves are balanced on each pair of chopsticks. Pour the limoncello into the shot glasses, letting some extra pour over into the watermelon. Grab your friends and have everyone beat on the table around the watermelon until the kiwi shot glasses fall into the drink. Serve with the watermelon juice ice cubes.
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