Melt the butter in a large skillet over medium heat. Add the cubed beef and cook slowly, stirring occasionally, until browned and tender. Meanwhile, dissolve the beef bouillon cubes in hot water to create a rich broth.

In a separate bowl, whisk the flour into the prepared broth until completely smooth and free of lumps. Once the beef is cooked, pour in the flour mixture along with the sour cream, chopped onion, and sliced mushrooms. Stir gently to combine, ensuring the sauce evenly coats the beef. Season with salt and pepper to taste.

Reduce the heat to the lowest setting and allow the mixture to warm through for about 20 minutes, stirring occasionally. Avoid simmering or boiling to maintain the creamy consistency of the sauce.

Meanwhile, cook the egg noodles according to the package instructions until tender. Drain well and serve hot, topped with the creamy beef stroganoff.