Place chicken into a 6-qt slow cooker. Stir in 1 1/2 cups Caesar dressing, chicken broth, garlic powder and onion powder; season with salt and pepper, to taste.
Cover and cook on low heat for 4 hours. Remove chicken from the slow cooker and shred, using two forks, before returning to the pot; drain excess liquid.
Stir in remaining 1/2 cup Caesar dressing, 1/4 cup Parmesan and parsley. Cover and cook on high heat for 15-30 minutes, or until hot.
Leaving a 1-inch border all around, layer each tortilla with chicken mixture, romaine lettuce, croutons and remaining Parmesan. Fold in sides by about 1 inch, then roll up tightly from the bottom.