01 - Combine broccoli florets, diced onion, carrots, celery, and garlic in the slow cooker. Pour in vegetable broth, ensuring vegetables are submerged.
02 - Cover and cook on low heat for 4 hours until vegetables are completely tender and easily pierced with a fork.
03 - Melt butter in a small saucepan over medium heat. Whisk in flour and cook for 1-2 minutes until bubbling and lightly golden, being careful not to brown.
04 - Gradually whisk half-and-half into the roux, stirring constantly until smooth and thickened, approximately 3-4 minutes.
05 - Pour cream mixture into slow cooker and stir to incorporate. Use immersion blender to partially puree until reaching desired consistency, leaving some texture if preferred.
06 - Stir in shredded cheddar cheese, salt, black pepper, smoked paprika, and nutmeg. Continue stirring until cheese is completely melted and soup is velvety smooth.
07 - Taste and adjust seasoning as needed. Serve hot, garnished with additional shredded cheese or accompanied by crusty bread.