Combine first 3 ingredients and 1/2 teaspoon salt in a large saucepan over medium-low heat. Cover and cook, stirring often, 10 minutes or until vegetables are soft. (Do not brown.) Spread mixture into a single layer on a baking sheet. Refrigerate 15 minutes or until thoroughly chilled.
Place cucumber mixture, 2 1/2 avocados, and remaining 1 1/2 teaspoons salt in a blender. (Cover remaining avocado half tightly with plastic wrap to prevent browning.) Add cold water and next 4 ingredients; process until smooth. Pour mixture into a bowl; cover surface with plastic wrap. Chill 2 hours.
Thinly slice remaining avocado half. Divide gazpacho evenly among 4 soup bowls. Top with avocado slices and Sourdough Croutons. Garnish, if desired.