In a large pot, melt butter over medium heat. Sauté onion and garlic until fragrant and translucent.
Add diced potatoes and broth to the pot. Bring to a boil, then reduce heat and simmer until potatoes are tender.
Stir in broccoli florets and cook for 5-7 minutes until bright green and tender.
Use an immersion blender to puree the soup to your desired consistency, or leave it chunky.
Stir in heavy cream and shredded cheddar cheese until melted and smooth.
Season with salt and pepper to taste. Serve warm with crusty bread.