Season chicken breast with 1/2 tablespoon salt and 1 teaspoon pepper in each side (lesser amount if you prefer).
Heat oil in a medium sized frying pan and cook chicken in high heat until chicken is cook through- about 5 minutes each side.
Remove chicken from the pan, and let chicken continue cooking in its steam until it cools. Slice chicken into strips and set aside until ready to use.
In the same pan, add cooking oil and saute' onion in high heat until transparent.
Lower heat. Add heavy cream, milk and 1/2 cup of parsley.
Bring into a simmer and add in 1 cup of Parmesan cheese.
Continue to simmer in low heat while stirring constantly until the cheese melt into a creamy sauce.
Add in 8- 10 oz cooked broccoli and cooked pasta into the sauce and mix everything and let it simmer for another 3 minutes.
Season with salt and pepper.
Add chicken and serve while it's hot.