Combine strawberries and 1 cup buttermilk in a blender or food processor. Cover and blend or process until very smooth. Transfer to a medium bowl. Stir in shredded lemon peel and the chopped thyme. Cover and chill for 4 to 24 hours to blend flavors.
To serve, strain soup, discarding the shredded lemon peel and the chopped thyme. Stir in honey. Ladle chilled soup into small bowls. If desired, swirl 1½ teaspoons buttermilk into each serving and garnish with lemon peel strips and/or fresh thyme sprigs.