Cut 5 cucumbers into 3-inch chunks. Place half of cucumber chunks and 2 tablespoons honey in a blender or food processor; process until smooth. Pour pureed cucumber mixture through a cheesecloth-lined sieve into a bowl. Repeat procedure with the remaining chunks. Cover and chill at least 8 hours.
Peel, seed, and thinly slice remaining 6 cucumbers; place slices in a bowl. Add vinegar and remaining 2 tablespoons honey; toss well to coat. Cover and chill 8 hours or overnight.
Working with pureed cucumber mixture in sieve, press mixture lightly with a wooden spoon or rubber spatula to squeeze out juice; discard solids.
Place half of marinated cucumber slices, avocado, and 1 3/4 cups cucumber juice in a blender or food processor; process until smooth. Pour cucumber mixture into a bowl. Repeat procedure with remaining cucumber slices and 1 3/4 cups cucumber juice; reserve any remaining juice for another use. Stir in chopped dill, salt, and pepper. Place 1 1/2 cups soup into each of 6 bowls. Garnish with cracked black pepper and dill sprigs, if desired.
Wine note: Green, vegetal flavors, like those found in this soup, call for sauvignon blanc's distinctive, herbaceous character. The wine's grassy, citrus qualities bring out the soup's fresh, crisp flavors. A good value from California is Dry Creek Vineyard Fumé Blanc ($13.50). -Jeffery Lindenmuth
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