Place the chicken breasts directly into the crockpot. Season generously with salt and pepper, then pour in chicken broth and add the minced garlic. Cover and cook on low for 3 to 4 hours until the chicken is tender and easily shreddable, filling your kitchen with the aroma of garlic and simmering broth.
Once cooked, shred the chicken right in the crockpot using two forks. The chicken should be fall-apart tender, and the mixture will smell fragrant and garlicky. Stir to combine the shredded chicken with the broth and garlic.
Pour in the heavy cream and sprinkle in the grated Parmesan cheese. Stir well to combine, then cover and cook on high for another 20-30 minutes, stirring occasionally. The sauce will thicken, become smooth, and take on a creamy, cheesy sheen.
Meanwhile, cook your pasta in a large pot of salted boiling water until al dente according to package instructions. Drain well and set aside.
Add the cooked pasta to the crockpot and stir gently to coat all the noodles with the creamy Alfredo sauce. Let sit for 5 minutes to allow the flavors to meld and the sauce to thicken slightly further.
Stir in the butter for extra richness, then taste and adjust seasoning with more salt and pepper if needed. For a fresh touch, sprinkle chopped parsley or basil on top before serving.
Serve hot, making sure each serving is generously coated with the velvety, cheesy sauce. Enjoy the comforting aroma and tender, flavorful chicken in every bite.