Spray cooking spray in the insert of a large 7 quart slow cooker. Place the broccoli, carrots, onion and garlic into the bottom of slow cooker. Stir to combine. Next, add the cubed cream cheese, oregano and chicken broth. Cover with lid and cook on low heat for 4 to 6 hours. OR on high heat 3 hours.
Remove lid and pour in milk and heavy whipping cream. Stir. Using an immersion blender, puree soup until it is smooth. (If you don't have an immersion blender you can carefully transfer hot soup by one cup batches to a blender and blend until smooth. Return soup to slow cooker after.)
Let soup heat back up in slow cooker for another 20 to 30 minutes. Stir in salt, pepper and one cup of sharp cheddar cheese.
Serve soup warm with additional cheese, if desired. Enjoy!