In a large pot, melt the butter over medium heat.
Add the diced onion and cook for 2–3 minutes until softened.
Stir in the minced garlic and cook for another minute until fragrant.
Add the diced potatoes and broccoli florets to the pot.
Pour in the broth and bring to a boil.
Reduce the heat to low and simmer for about 15 minutes, or until the potatoes are tender.
If you prefer a smoother soup, use an immersion blender to blend the soup to your desired consistency. Alternatively, you can transfer part of the soup to a blender, blend it, and return it to the pot.
Stir in the heavy cream, shredded cheddar cheese, salt, and pepper.
Cook for another 5 minutes, stirring until the cheese has melted and the soup is creamy.
Serve the soup hot with crusty bread or a side salad.