Lightly coat the inside of the slow cooker with nonstick spray and place the chicken breasts in an even layer on the bottom.
In a medium bowl, whisk together the cream of chicken soup, mayonnaise, lemon juice, curry powder, salt, and pepper until smooth.
Pour the sauce mixture over the chicken, making sure it is evenly covered. Cover and cook on High for 2 to 3 hours or Low for 4 to 5 hours, until the chicken is tender.
Shred the chicken directly in the slow cooker using two forks, mixing it into the sauce.
Add the broccoli florets and stir gently to combine.
Sprinkle the shredded cheese evenly over the top, cover again, and cook on High for about 30 minutes, until the broccoli is tender and the cheese is melted.
Garnish with parsley if desired and serve warm.