01 - Arrange the chicken breasts in an even layer at the bottom of your slow cooker insert.
02 - Distribute the chopped onions, minced garlic, and broccoli florets evenly over the chicken.
03 - In a medium mixing bowl, whisk together the chicken broth, softened cream cheese, sour cream, milk, Dijon mustard, paprika, salt, and black pepper until completely smooth and no lumps remain.
04 - Pour the prepared sauce mixture evenly over the chicken and vegetables, ensuring all pieces are coated.
05 - Cover and cook on high setting for 4 hours or low setting for 6-7 hours, until the chicken reaches an internal temperature of 165°F and is tender throughout.
06 - Using two forks, shred the chicken directly in the slow cooker or slice into bite-sized pieces. Stir thoroughly to distribute the meat throughout the sauce.
07 - Stir in the shredded sharp cheddar cheese until fully melted and incorporated into the creamy mixture.
08 - If a thicker consistency is desired, combine the cornstarch with 2 tablespoons cold water to create a slurry. Stir into the slow cooker and cook for an additional 15-20 minutes until the sauce has thickened.
09 - Taste the dish and adjust salt or pepper as needed. Serve immediately, garnished with additional shredded cheddar or fresh herbs if desired.