Place diced chicken breasts in the bottom of the crock pot. Season with salt, black pepper, and minced garlic. Pour chicken broth over the chicken, adding a dollop of unsalted butter. Set the crock pot on low heat.

Cover the crock pot and cook on low for 4 to 5 hours until the chicken is tender and easily shreds.

Stir in the cubed cream cheese and heavy cream into the chicken mixture after cooking time. Allow cream cheese to melt for about 15 minutes, and mix until smooth.

Meanwhile, bring a pot of salted water to boil. Cook fettuccine until al dente, approximately 8 to 10 minutes. Drain and set aside.

Gently stir in the cooked fettuccine and broccoli florets into the sauce in the crock pot and mix gently.

Cover and let everything cook on low heat for an additional 20 to 30 minutes.

Serve warm from the crock pot, garnished with extra Parmesan cheese, if desired.