In skillet, brown chicken breasts in olive oil. Place chicken in crockpot. Add green onions, garlic, tomatoes, and basil. Cover and cook on Low 7 to 9 hours. Remove chicken and cut into pieces. Return chicken pieces to pot.
Stir in cream, egg yolks, and parmesan cheese. Cover and cook on high 30 minutes to thicken. While sauce is thickening, cook fettuccine according to package directions; drain. Add fettuccine, peas and mushrooms. Cover and cook on high 30 to 60 min.