Melt butter in a medium pot or Dutch oven over medium heat. Add onion and sauté 3-5 minutes until translucent. Add garlic and flour and cook 1-2 minutes until fragrant.
Slowly drizzle in chicken broth, stirring constantly until evenly incorporated into flour. Add half and half, shredded carrot, broccoli, and pinch of nutmeg and bring soup to a simmer over medium heat. Reduce heat to medium-low and allow to simmer 8-10 minutes until broccoli is tender, stirring occasionally.
Scoop out 1/2 cup soup and blend smooth in a standard blender or with an immersion blender until smooth. Add back to soup pot and fold in cheddar until melted. Season soup with salt and pepper to taste and serve warm. Enjoy!
Notes
Storing InstructionsStore soup in refrigerator up to 6 days. Soup may also be frozen up to 2 months.