Add the broccoli florets, diced onion, diced carrots, chicken broth, minced garlic, salt, and black pepper to the slow cooker. Stir to combine.
Cover and cook on low for 6 hours or on high for 3 hours until the vegetables are soft.
In a small bowl, whisk the cornstarch with 2 tablespoons of cold water to form a slurry. Stir the slurry into the soup.
Pour in the milk and add the shredded cheddar cheese. Stir until the cheese melts fully and the soup thickens.
Taste and adjust salt or pepper if needed before serving.