Combine broth and cornstarch, stirring with a whisk.
Melt butter in a large saucepan over medium-high heat. Add onion; sauté 3 minutes. Add garlic; sauté 30 seconds. Stir in broth mixture, corn, salt, and pepper; bring to a simmer. Cook 10 minutes, stirring frequently (do not boil). Place half of corn mixture in a blender, and process until smooth. Pour pureed corn mixture into a large bowl. Repeat procedure with remaining corn mixture. Strain corn mixture through a sieve into a large bowl; discard solids. Stir in milk and half-and-half; chill thoroughly. Let stand 30 minutes at room temperature; stir well.
Ladle 2/3 cup soup into each of 8 bowls; top each serving with 3 tablespoons crab, about 2 teaspoons avocado, and about 1 teaspoon basil.