In a large pot, melt butter over medium heat. Add onion and garlic, sautéing until soft.
Add broth, potatoes, and broccoli to the pot. Season with salt, pepper, and nutmeg. Bring to a boil, then reduce to a simmer and cook until vegetables are tender, about 10-15 minutes.
In a separate bowl, whisk together milk and flour until smooth. Gradually stir into the soup. Cook until the soup thickens, about 5 minutes.
Remove from heat. Stir in cheddar cheese until melted and smooth. For a smoother soup, use an immersion blender to puree directly in the pot to your desired consistency.
