Put the avocado pulp, cucumber and zucchini with the skin, garlic clove and buttermilk in a saucepan. Process with a very good hand blender to a creamy, rather thick mass. Stir in the spices and olive oil and season to taste.
Clean the strawberries and place them in a second saucepan with the tomatoes. Also puree. Heat slowly, but do not boil.
First serve the cold buttermilk soup in glasses, then carefully but lively add the warm tomato soup. Garnish with fresh tomatoes and basil leaves and grind fresh pepper over them.
Serve immediately, preferably with long latte macchiato spoons. Bread sticks go well with it.