Lightly grease the slow cooker with olive oil.
Place chicken breasts in the bottom of the slow cooker.
Pour in chicken broth and sprinkle with minced garlic, Italian seasoning, salt, black pepper, and red pepper flakes.
Cover and cook on low for 3-4 hours or on high for 2-3 hours until chicken is cooked through.
Remove chicken and shred it with two forks. Return shredded chicken to the slow cooker.
Add heavy cream, Parmesan cheese, and broccoli florets. Stir to combine.
Cover and cook an additional 20-30 minutes on low until broccoli is tender and sauce is creamy.
Serve over cooked pasta or noodles.