Step 1: Melt the butter or heat the olive oil in a large pot or Dutch oven over medium heat. Add the chopped onions and cook until softened and translucent, about 5-7 minutes.
Step 2: Stir in the minced garlic and cook for another minute until fragrant, being careful not to burn it.
Step 3: Add the chopped zucchini and diced potato to the pot. Pour in the vegetable or chicken broth. Bring the mixture to a boil, then reduce the heat, cover, and simmer for 15-20 minutes, or until the zucchini and potatoes are very tender.
Step 4: Carefully remove the pot from the heat. Using an immersion blender, blend the soup directly in the pot until it is completely smooth and creamy. Alternatively, transfer the soup in batches to a regular blender, blending until smooth (vent the lid slightly and cover with a kitchen towel when blending hot liquids).
Step 5: Stir in the heavy cream (or coconut milk), fresh dill, salt, and black pepper. Taste and adjust seasonings as needed.
Step 6: Gently heat the soup over low heat for a few minutes until warmed through. Do not boil after adding the cream. Serve hot, garnished with extra fresh dill, a swirl of cream, or homemade croutons.