Rub olive oil evenly over chicken breasts. Sprinkle Italian seasonings, kosher salt and pepper on chicken and place in a single layer in slow cooker. Spread pesto and sliced red onions on top of chicken.
Cook on low for 5-6 hours, or until chicken is fully cooked and can be shredded easily with 2 forks.
Cook pasta for 3-4 minutes less than time shown on package instructions.
Meanwhile, remove the chicken from slow cooker and shred using 2 forks. Return the chicken to the slow cooker and add partially-cooked pasta, mozzarella, smoked gouda, Parmesan, cherry tomatoes and fresh basil; stir until well combined.
Continue cooking on low for 15-20 more minutes, or until cheeses have fully melted.