In a large, deep skillet or a dutch oven with a tight-fitting lid, heat the olive oil over medium. Once hot, add the chicken, thyme, smoked paprika, garlic powder, salt, and pepper. Continue to cook, breaking up the meat with a spoon, until it is fully browned on all sides, 3 to 4 minutes.
Add the sliced mushrooms. Continue to cook until the mushrooms begin to soften, about 5 to 6 minutes. Sprinkle the flour over the top, then stir so that it coats the chicken and mushrooms.
Add about one-third of the chicken stock. Stir and work the flour and any browned bits off of the bottom of the pan. Add the rest of the stock and the egg noodles and cover the pan. Bring the liquid to a boil, then immediately remove the lid and stir the pan. Re-cover, then reduce the heat to a low simmer. Let simmer until the noodles are al dente and most of the liquid is absorbed, about 7 minutes, stirring the noodles and replacing the lid every few minutes. If at any point the liquid drops below a gentle simmer, increase the heat slightly.
Once the noodles are tender, remove the pan from the heat and let sit 1 minute to cool slightly. Stir in the room-temperature Greek yogurt. Taste and adjust seasonings as desired. Sprinkle with fresh parsley and serve hot.
TO STORE: Refrigerate stroganoff in an airtight storage container for up to 3 days.
TO REHEAT: Rewarm leftovers in a Dutch oven on the stovetop over medium-low heat. Add a splash of chicken stock as needed.
TO FREEZE: Freeze stroganoff in an airtight freezer-safe storage container for up to 3 months. Let thaw overnight in the refrigerator before reheating.