Pat the chicken breasts dry, then season both sides generously with salt and pepper. Heat the olive oil in your large skillet over medium-high heat until it shimmers. Add the chicken and sear for 4 to 5 minutes per side, until golden brown and cooked through, then set it aside on a plate.
In that same skillet, melt the tablespoon of butter over medium heat. Add the sliced mushrooms and let them cook undisturbed for a few minutes so they can brown properly. Stir occasionally until they release their juices and turn a deep golden color, about 5 minutes total.
Add the minced garlic, thyme, and oregano straight into the mushroom pan. Stir constantly for about a minute, just until the garlic turns fragrant and the herbs wake up. Don't let the garlic sit too long or it will turn bitter fast.
Pour the chicken broth into the skillet, scraping up all those browned bits stuck to the bottom. Bring it to a gentle simmer and let it reduce by about half, which takes roughly 5 minutes. This step is where most of the deep flavor in the sauce comes from.
Lower the heat slightly and pour in the heavy cream, stirring to combine. Let the sauce simmer gently until it thickens just enough to coat the back of a spoon, about 3 to 4 minutes. Taste it here and adjust the salt and pepper if needed.
Nestle the seared chicken breasts back into the sauce along with any juices that collected on the plate. Spoon the sauce over the top and let everything warm through together for a couple of minutes. This lets the chicken soak up a bit more flavor before serving.
While the sauce simmers, boil the egg noodles in well-salted water according to the package directions. Drain them well, then toss immediately with the 2 tablespoons of butter so it melts through every strand. Keep them warm until you're ready to plate.
Spoon a bed of buttered noodles onto each plate, then top with a chicken breast and a generous ladle of mushroom sauce. Sprinkle fresh parsley and grated Parmesan over everything right before serving. Serve immediately while it's still hot and creamy.