Bring a large pot of salted water to a boil for the noodles. Set the sour cream on the counter now so it comes to room temperature.
Trim the chuck roast and cut it into ½ inch cubes. In a bowl, toss the beef with the salt, pepper, garlic powder, and smoked paprika, then sprinkle over the flour and toss again until lightly coated.
Heat the olive oil in a large skillet or Dutch oven over medium-high heat. Add the beef in a single layer, working in two batches if needed, and sear 3 to 4 minutes per batch until well browned. The beef will not be cooked through. Transfer to a plate.
Reduce the heat to medium. Add the butter, mushrooms, and onion to the same pan. Cook 7 to 8 minutes, until the mushrooms are browned and the onions are soft.
Stir in the garlic and cook 30 seconds, just until fragrant.
Pour in the beef broth, scraping up all the browned bits from the bottom of the pan. Stir in the Worcestershire sauce and whole grain mustard.
Return the beef and any accumulated juices to the pan. Bring to a gentle simmer, cover, and cook 25 minutes, until the beef is tender enough to give when pressed against the side of the pan. Cook the egg noodles while the beef simmers.
Remove the pan from the heat entirely and let it rest 1 minute.
Put the room temperature sour cream in a small bowl. Stir in 3 to 4 spoonfuls of the hot sauce, one at a time, until smooth and warmed. Pour the tempered sour cream into the pan and stir to combine. Do not return the pan to a boil.
Bring a large pot of salted water to a boil for the noodles. Set the sour cream on the counter now so it comes to room temperature.
Serve over the cooked egg noodles, or toss the noodles directly into the pan and stir to coat.