Rinse your mushrooms under a cool stream of water while brushing off the dirt with a vegetable brush or (wipe with a damp paper towel). Pat the mushrooms dry with a paper towel, slice them and set aside.
Peel your onion and slice it thinly.
Peel your garlic clove and press it with with a garlic press (or chop it finely).
Pound your steak to about 1/3-inch thick using a meat mallet or the bottom of a heavy skillet. Use a knife or kitchen scissors to trim off excess fat. Slice the beef into strips (slice in the opposite direction of the grain to help make it more tender.) Cut any long strips in half. Wash your hands well.
Prepare the seasoning blend by mixing the paprika and mustard with 1/4 teaspoon salt and 1/4 teaspoon pepper.
Fill a pasta pot 2/3 full with hot water and set it on the stove without any heat yet.
In an extra-large skillet, melt two tablespoons of butter over medium-high heat. Add the beef strips to the pan in a single layer. Sprinkle on the seasoning blend.
Quickly brown the meat on one side, then flip it over to brown the other side for about 30 seconds. The meat will still have some pink on the edges but will cook more later. Use a slotted spoon to transfer the beef to a platter and cover it with foil.
Add two more tablespoons of butter to the pan and let it melt. Add your onions and mushrooms but hold off on the garlic. Stir to combine. Add 1/4 teaspoon salt and 1/4 teaspoon pepper. Stir again and let cook, stirring occasionally, until the onions are soft and golden, the mushrooms are golden brown and all the liquid has evaporated. This should take around 15 minutes.
When the mushrooms and onions are golden brown, stir your pressed garlic into the mushrooms and let it cook for a minute. Stir in 3 tablespoons of flour and cook for another minute.
Deglaze the pan by pouring in 1/2 cup white wine and using a wooden or plastic spoon to scrape all the bits off the bottom of the pan. Stir everything for a minute, then stir in 1 1/2 cups beef stock.
Bring the mixture to a boil, then lower the heat and let the pan simmer for five minutes.
While that's simmering, add a teaspoon of salt to your pot of water for the egg noodles. Cover the pot with a lid and place the pot over high heat so it can boil.
After the mushroom mixture has simmered for five minutes, stir in the sour cream and bring the sauce to a simmer. Let the sauce simmer over low heat for 5-10 minutes, until the sauce is thickened.
While the mushroom sauce is simmering, cook your egg noodles in the boiling water. Cook them until al dente (check on them a minute or two before the package directions say they're done.) Drain the egg noodles in a colander in the sink, keeping just a bit of the cooking water in the pot. Return the drained noodles to the pot and stir in 3 tablespoons of butter.
When the mushroom sauce is thickened, add the beef to the sauce and give it a stir. Let the beef cook for 2-3 minutes more. (You can cut into a strip of beef to see if it is cooked enough for you. It needs to have some pink inside in order to be tender. Keep in mind the beef will continue cooking after you turn off the heat.)
Serve the Beef Stroganoff over the egg noodles. Serve with red pepper flakes at the table if desired.
Store leftover noodles separately from the Beef Stroganoff. Refrigerate leftovers for up to four days.