Bring a large pot of salted water to a boil; add the pasta and cook according to package directions.
While the pasta is cooking, heat 1 tablespoon of olive oil in a large pan over medium heat.
Add the mushrooms to the pan and season with salt and pepper to taste. Cook for 4-5 minutes stirring occasionally, until tender and browned. Stir in the kale and cook for 1-2 minutes more, or until kale is just wilted.
Remove the vegetables from the pan and place on a plate. Cover with foil to keep warm.
Wipe out the pan with a paper towel and heat the remaining tablespoon of olive oil over medium high heat.
Add the chicken to the pan and season with and pepper. Cook for 5-6 minutes, stirring occasionally, or until cooked through.
Add the reserved vegetables to the pan and stir to combine. Add the tomatoes and cook for 1 minute.
Drain the pasta, reserving 1/4 cup of cooking water and return pasta to the pot it cooked in. Turn the heat on medium high and add the cream along with salt and pepper to taste. Cook for 3-4 minutes or until sauce has started to thicken. Add pasta water if needed to thin the sauce.
Place the chicken and vegetable mixture on top of the pasta and sprinkle with parsley. Serve immediately.