Heat olive oil and butter in a large, heavy pot or Dutch oven over medium heat. Combine flour, salt, and black pepper in a bowl and toss beef stew meat in seasoned flour. Brown the beef in the hot oil and butter, stirring often, and remove meat from pan.
Pour white wine into pan and scrape up and dissolve any small bits of browned food; stir onion and garlic into white wine. Cook until onion is translucent, stirring often, about 5 minutes. Return browned beef to pan. Stir ketchup, Worcestershire sauce, and juice from canned mushrooms with beef mixture. Reduce heat to low, cover pan, and simmer until beef is tender, about 3 hours.
Mix button mushrooms and sour cream into beef mixture and heat through, about 5 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. Serve Stroganoff over cooked egg noodles.
