For the potatoes, you can peel if you want, certainly not required, dice the potatoes to about 3/4 inch cubes. Place potatoes in a pot of water and bring to a boil. Cook for about 5 minutes until just nearly fork tender. Drain potatoes and set aside.
Heat 1 tablespoon of oil in a large non stick pan, when hot, add the onion, garlic, and mushrooms and saute until the mushrooms are just starting to brown. Then add the chicken and season with 1/2 teaspoon of salt, pepper, and the thyme. Saute for 3-4 minutes until the chicken is nearly cooked through. Remove everything from the pan and set aside.
Same pan, quickly wipe that out with a paper towel then add the remaining oil and heat over medium high heat. When hot, add the potatoes and let cook without stirring for 5-6 minutes, then add 1/2 teaspoon salt, stir the potatoes and cook, stirring often until well browned, about 4-5 minutes.
Stir in the chicken and mushrooms mixtures, cream, and parsley. Cook until the chicken is heated through.