In a pot, melt butter and sautee garlic for 30 seconds.
Sprinkle flour and whisk until no clumps remain.
Add milk little by little, constantly whisking to prevent lumps.
Add water and broth (or bouillon cube). Mix until the cube is melted.
Add the broccoli and bring to a simmer. Cook for 15 minutes and stir in the cream.
Add the carrots.
After 5 minutes, remove from heat and use an immersion blender and blend the soup to your desired consistency (skip this step if you want a chunky soup). If the soup is too thick for your liking, please feel free to add water then simmer again.
Stir in cheese and allow to melt.
Season with salt and pepper to taste.
Serve hot with more cheese on top, crusty bread or croutons.