Season beef with salt, pepper, and Spanish paprika.
Melt butter in a large skillet over medium heat. Saute onions and mushrooms in melted butter until onions are tender, 5 to 7 minutes; transfer to a bowl, retaining some of the butter in the skillet.
Cook and stir beef in retained butter until lightly browned, 5 to 7 minutes.
Stir 2/3 cup beef broth, white wine, garlic, and ketchup into the beef mixture; season with salt and pepper. Place a cover on the skillet and cook mixture at a simmer for 15 minutes.
Bring a large pot of lightly salted water to a boil. Cook egg noodles in the boiling water, stirring occasionally until cooked through but firm to the bite, about 5 minutes; drain.
Whisk remaining beef broth and flour together in a bowl; add to beef mixture. Bring the mixture to a boil, stirring continually, and boil for 1 minute. Reduce heat to low, add sour cream, and stir until smoothly incorporated. Ladle over egg noodles and garnish with paprika.