In a large pot, melt the butter over medium heat.

Add the diced onion and minced garlic to the pot and sauté until the onion becomes translucent, about 3-4 minutes.

Carefully add the vegetable or chicken broth to the pot.

Stir in the diced potatoes and bring the mixture to a boil.

Once the potatoes are tender, add the broccoli florets.

If you prefer a smoother texture, use an immersion blender to puree the soup partially.

Add the shredded cheddar cheese and heavy cream, stirring until the cheese melts and the soup is creamy.

Season with salt and pepper to taste, then ladle the soup into bowls.