Season and load the slow cooker: Add onion, garlic, chicken broth, Italian seasoning, salt, pepper, and red pepper flakes to the slow cooker. Stir to combine. Nestle the chicken breasts into the liquid.
Cook the chicken: Cover and cook on Low for 3 to 4 hours, or on High for 1.5 to 2 hours, until the chicken is cooked through and easily shreds.
Avoid overcooking; juicy chicken makes a better sauce.
Shred the chicken: Remove the chicken to a cutting board and shred with two forks. Keep the cooking liquid in the slow cooker. Return the shredded chicken to the pot.
Thicken the base: In a small bowl, whisk the cornstarch with 2 tablespoons of the milk to make a slurry.
Stir the slurry into the slow cooker. Add the light cream cheese if using. Cover and cook on High for 10 to 15 minutes to slightly thicken.
Cook the pasta: Break the fettuccine in half and add it to the slow cooker, pressing it down into the liquid and chicken so it’s mostly submerged.
Drizzle with olive oil or dot with light butter to prevent sticking. Cover and cook on High for 20 to 30 minutes, stirring gently every 8 to 10 minutes, until the pasta is al dente. If it looks dry, add 1/4 cup hot water or broth at a time.
Finish the Alfredo sauce: In a bowl, whisk together the Greek yogurt, remaining milk, and Parmesan until smooth.
Turn the slow cooker to Warm. Stir in the yogurt mixture gradually to avoid curdling. Taste and adjust seasoning with more salt, pepper, and a squeeze of lemon if desired.
Rest and serve: Let the pasta sit on Warm for 3 to 5 minutes to set.
Garnish with parsley and extra Parmesan. Serve right away while creamy.