Melt butter in a large pot over medium heat, add diced onions and sauté for 3-4 minutes until translucent. Stir in minced garlic and cook for 30 seconds.

Add diced potatoes and chicken stock to the pot, bring to a gentle boil, then lower heat and simmer for 10-15 minutes until potatoes soften.

Add broccoli florets and simmer for another 5-7 minutes until broccoli is vibrant and tender yet slightly crisp.

Using an immersion blender, blend part of the soup for a creamy consistency while leaving some chunks for texture.

Stir in shredded cheddar cheese and milk, mixing until cheese is melted and soup is creamy. Heat through on low for 2-3 minutes.

Season with salt and pepper to taste, ladle into bowls and serve hot, optionally with crusty bread.