• Cooked whole-grain egg noodles, for serving
Season the meat with 1/4 teaspoon each salt and pepper. Heat 1 tablespoon oil in a large skillet over medium-high heat. Once the oil shimmers, add the beef and cook for 1 to 2 minutes, until seared but still pink inside. Transfer the meat with its juices to a plate.
Add the remaining 2 tablespoons oil to the skillet and warm over medium heat. Add the shallot and cook for about a minute, stirring, until softened. Add the mushrooms, and then the garlic, and cook for 8 to 10 minutes, stirring occasionally, until the mushrooms have released their water and it has evaporated.
Sprinkle the mushrooms with the flour and stir until well combined. Add the beef broth and, stirring, bring to a boil. Reduce the heat to low; add the remaining 1/2 teaspoon salt and 1/4 teaspoon pepper. Cook for about 5 minutes, until the mixture thickens and reduces slightly, then stir in the mustard until well incorporated. Add the sour cream, stirring until well blended.
Return the meat and any accumulated juices to the pan; cook for 1 to 2 minutes, until the meat is just warmed through, but still medium-rare.