Slice the fresh button mushrooms into thin slices. Finely grate the cheese.

Add the oil to a skillet and heat it over medium heat. When the oil gets hot, add the ground beef and saute it with a wooden spoon, stirring frequently to break up the big chunks of meat into smaller ones.

Once the beef is no longer pink, add the sliced mushrooms. Continue sauteing, stirring often, until the mushrooms release their moisture and they become pale brown. This step may take several minutes, depending on the thickness of the mushrooms.

Sprinkle all-purpose flour and continue sauteing the meal for about one more minute, stirring frequently. Make sure the ground beef and mushrooms are well-coated with the flour.

Add the dried thyme, parsley flakes, salt, and pepper. Stir to combine. Then pour in the milk, stir again, and let it simmer for 2 to 3 minutes. Stir in the allium-free mustard and Greek yogurt.

Simmer the sauce for up to 5 minutes, stirring occasionally, until it thickens. Taste the sauce, and adjust salt and pepper if necessary.

While the sauce is simmering, cook the pasta, according to the package instructions. If a range of cooking times is listed, use the minimum time. Then drain the pasta.

Add the cooked pasta to the skillet with the Stroganoff sauce. Stir to coat. If the sauce feels too thick, add a splash of milk. Stir in half of the grated cheese.

Transfer to a baking dish and sprinkle the remaining grated cheese over the top.