Heat oil in a small skillet over medium heat. Add garlic and cook, stirring, until golden, about 2 minutes; transfer to slow cooker.
Add onion, bell pepper and mushroom. Put chicken on top; sprinkle with salt and pepper. Pour in crushed tomatoes; cover and cook for 4 hours on high or 8 hours on low. Chicken should be very tender.
Bring a pot of salted water to a boil and cook rotini according to package directions until al dente. Drain and transfer to a large serving bowl.
Transfer chicken to 4 plates. Skim fat from surface of sauce and discard. Stir parsley into sauce. Spoon some sauce over chicken. Serve remaining sauce with pasta and cheese.