Melt butter in a large saucepan over medium heat; stir in onion. Cook and stir until onion has softened and turned translucent, about 5 minutes. Add diced potato, zucchini, basil, thyme, rosemary, and white pepper; continue to cook and stir until zucchini is soft, about 5 minutes.

Add broth and bring to a simmer; cook until potatoes are soft, about 15 minutes.

Puree soup with an immersion blender until smooth; add milk and stir until heated through, without boiling. Stir in potato flakes if needed to thicken the soup. Season to taste with soy sauce and garnish with dill weed.