Fold two 18-in. square pieces of heavy-duty foil into thirds. Crisscross strips and place on bottom and up sides of a 6-qt. slow cooker. Coat strips with cooking spray., In a 6-qt. stockpot, cook chicken over medium heat until no longer pink, 6-8 minutes, breaking into crumbles; drain. Set chicken aside., In same pot, heat oil over medium-high heat. Add mushrooms, onion and carrots; cook and stir just until tender, 6-8 minutes. Add garlic, Italian seasoning, salt and pepper; cook 1 minute longer. Stir in wine. Bring to a boil; cook until liquid is reduced by half, 4-5 minutes. Stir in cream, cream cheese, cheddar and Gouda cheeses. Return chicken to pot. In a large bowl, combine egg, cottage cheese and basil., Spread 1 cup meat mixture into slow cooker. Layer with 3 noodles (breaking noodles as necessary to fit), 1 cup meat mixture, 1/2 cup cottage cheese mixture and 1 cup mozzarella cheese. Repeat layers twice. Top with remaining meat mixture and cheese. Cook, covered, on low until noodles are tender, 3-4 hours. Remove slow cooker insert and let stand 30 minutes. If desired, sprinkle with additional basil. Using foil strips as handles, remove lasagna to a cutting board or platter.