Cook pasta in a pot according to package directions, being sure not to overcook it. Drain and rinse in cold water to cool. Toss in 1 tablespoon olive oil and set aside. Place chicken in a large pot or dutch oven and cover in chicken stock. Bring to a boil, then simmer chicken, covered, for 30 minutes. Turn off heat and leave covered for 30 minutes. Remove chicken from pot and shred meat. Discard bones and set meat aside.
Dice canned tomatoes and return them to their juice. Set aside. Heat a small skillet over medium high heat. Add olive oil and oregano and turn off heat, stirring over the next minute to keep oregano from burning. Set this aside. Either pour off chicken broth into a separate container or use a new pot to saute onion, green pepper, celery, and jalapenos in 1 tablespoon olive oil over medium heat until tender and golden brown, about 10 minutes. Add chicken broth, shredded chicken, and tomatoes with their juice. Bring to a boil, then reduce to a simmer. Add cooked pasta, cream, and all the oregano and olive oil from the small skillet. Stir to combine. Turn off heat. Serve with lots of Parmesan sprinkled on the top--the more the better! Crusty Italian bread is fantastic to serve with this yummy soup!