In a large pot, sauté onion in butter until soft and slightly golden.

Add water, soup mix, potato, chopped broccoli, half the corn (about 3/4 cup), and salt. Bring to a boil and then lower the heat to a simmer. Cook for about 40 to 45 minutes, or until vegetables are soft.

Add milk and blend soup with an immersion blender until smooth and creamy. Add remaining 3/4 cup corn kernels and broccoli florets. Break some of the larger florets into smaller pieces.

Bring soup back to a boil and cook for an additional 12 to 15 minutes, or until broccoli begins to soften. Season with freshly ground black pepper.