Pour the chicken broth, dijon mustard, paprika, salt, and white pepper into a slow cooker and stir to combine. Add the broccoli.

Cook the broccoli on low for 5 to 6 hours or until the broccoli has reached the desired tenderness.

Sauté the carrots and onions with butter in a large skillet over medium heat. About 5 minutes or until the onions are translucent and tender. Add the garlic to the skillet and sauté for 30 seconds more.

Stir in the flour and cook for 2 minutes, stirring frequently.Slowly add the heavy cream to the skillet and then add the cheese, stirring continuously, just until melted. Pour the cheese sauce into the slow cooker and stir gently.

Cook the soup in the slow cooker for 30 more minutes on low (about 20 on high) to allow the broth to thicken. Garnish the soup with additional cheese if desired and serve warm.