Season the chicken with salt & pepper & place in a zip top bag. Pour the flavored oil over the chicken & set aside (do not refrigerate).
Place the diced vegetables in a bowl & pour the Greek dressing over them. Set aside (do not refrigerate).
Bring the heavy cream to a boil over medium high heat. Reduce the heat to medium low & simmer until reduced by 1/3 and thickened whisking often. Half way through reduction, season the cream with the fresh herbs, salt & pepper.
WHILE CREAM IS REDUCING: Cook rice as per pkg. directions. Add cheese & stir. Cover & set aside.
Saute the vegetables to tender crisp & add to the rice. Saute the chicken in the same skillet used for the vegetables to just done. Add the chicken to the reduced cream sauce & stir. Serve the chicken over the wild rice with vegetables.