Heat oil in a large pot over medium heat. Cook and stir steak in hot oil until browned completely, about 5 minutes.
Stir water, ketchup, onion, Worcestershire sauce, brown sugar, paprika, mustard, garlic, salt, and pepper with the beef in the pot; bring to a boil, reduce heat to low, and cook at a simmer until meat is tender and the sauce thickens, 2 to 3 hours.
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.
