Bring a large pot of salted water to a boil and cook the egg noodles according to the package directions. Drain and set aside.
Melt the butter in a large skillet over medium heat. Add the diced onion and cook for 3 minutes until it begins to soften.
Stir in the garlic and sliced mushrooms. Cook for 6 to 7 minutes, stirring occasionally, until the mushrooms release their liquid and start to brown.
Sprinkle the flour over the mushroom mixture and stir for 1 minute to coat everything evenly.
Pour in the vegetable broth and add the paprika. Season with salt and pepper. Bring the mixture to a gentle simmer and cook for 3 minutes until it thickens slightly.
Remove the skillet from the heat and stir in the sour cream until the sauce is smooth.
Divide the cooked egg noodles among four plates. Spoon the mushroom sauce over the noodles and finish with a sprinkle of chopped parsley.