In a large pot over medium heat, melt the butter. Stir in onion and garlic and cook until onion is translucent, about 5 minutes. Stir in potatoes and carrots and cook 5 minutes more. Pour in the vegetable broth and bring to a boil. Stir in cauliflower/broccoli, cover, reduce heat and simmer until vegetables are tender, 15 to 20 minutes. Remove from heat.
Purée in batches in a blender , food processor, or with an immersion blender. Return to low heat and stir in milk, salt, pepper. Serve hot.