In a 6qt or 8qt slow cooker add chopped onion, minced garlic, broccoli, carrot, celery, Italian seasoning, red pepper flakes, and butter. Add the chicken broth and stir to combine. Cover and cook on high for 3-4 hours or on low for 4-6 hours.
In a large cup combine cream and cornstarch until smooth.
Uncover soup and add the cornstarch mix. Stir to combine. Cover and cook for 20 minutes on high.
Add the cheeses, salt, and pepper. Stir until the cheeses melt. Taste and adjust for salt and pepper if needed.
Serve warm and top with additional shredded cheese if desired. Enjoy!