In a large pot, melt the butter over medium heat. Add the onion and cook until soft, about 3 minutes. Stir in the garlic and cook for another 30 seconds.

Add the zucchini, potatoes, smoked paprika, salt, and pepper. Cook for 3 minutes, stirring occasionally.

Pour in the chicken broth and bring to a boil. Reduce heat and simmer for 10 minutes, or until the potatoes are tender.

Stir in the corn and milk. Simmer for 5 more minutes.

For a creamier texture, use an immersion blender to blend part of the soup right in the pot (or transfer about 1/3 to a blender and return to the pot).

Stir in the cheddar cheese (if using) until melted.

Ladle into bowls and sprinkle with chives or green onions. Serve hot!