In the insert of your slow cooker/crockpot, place your boneless skinless chicken breasts. Sprinkle ½ teaspoon kosher salt and ¼ black pepper evenly over the chicken. Sprinkle the entire contents of the dry Italian dressing mix evenly over the chicken as well.
Pour the chicken broth into the crockpot with the chicken and spices. Cover with the lid and turn on HIGH for 4 hours.
Once your chicken is done, remove it and shred it using 2 forks to pull it apart into bite-sized pieces.
Pour out all but 1 cup of the excess liquid that is remaining in the pot. Return the shredded chicken back to the crockpot insert and add back the reserved 1 cup of the seasoned cooking liquid.
Turn your crockpot to WARM while you cook your pasta and make your sauce.
Cook your pasta according to package directions (8 to 10 minutes) and drain when done.
In a medium saucepan, on medium heat, melt your butter. Once your butter is melted, whisk in the flour making sure there are no lumps.
Add your grated garlic, dried parsley, remaining ½ teaspoon salt, and ¼ teaspoon black pepper. Whisk to combine. Slowly add the half & half and heavy cream, making sure that you are whisking the entire time. This is very important to avoid any lumps in your final alfredo sauce.
Cook your cream mixture for 5 to 6 minutes, whisking often, until it starts to bubble and thicken. Once your cream mixture has thickened, turn off the heat and add your grated parmesan cheese. Stir to completely combine.
Add your cooked and drained pasta to your shredded chicken, then pour your alfredo sauce on top. Stir to combine. You can top your slow cooker Olive Garden chicken alfredo pasta with the fresh chopped parsley at this time if desired.