Bring a large pot of salted water to a boil. Add the egg noodles and cook until just before al dente.
Heat two tablespoons of butter in a large skillet over medium-high. Season the chicken with salt and sear in the pan for about three minutes on one side, then flip and sear another two until just golden brown. Remove the chicken from the pan and set aside.
To the skillet, add the remaining two tablespoons of butter. Add the mushrooms, along with a pinch of salt and let them brown in the pan for about five minutes.
Scoot the mushrooms to the side of the pan, and add a little bit of the stock. Then add the flour and whisk until it becomes a thick paste, just a few seconds. Keep pouring the stock into the pan, whisking as the sauce loosens a bit. Then slowly add the cream and whisk as the sauce becomes a creamy, velvety, buttery mixture. Add a good pinch of salt.
Transfer the cooked noodles to the sauce, and toss to coat. Nestle the chicken back into the mix and squeeze the juice from half the lemon over the whole dish.
Garnish with freshly chopped parsley and parmesan cheese, and serve.