Prepare the Beef: Season the cubed beef shoulder generously with sea salt and black pepper. Toss the seasoned beef with the flour until evenly coated.
Brown the Beef: Heat a splash of vegetable oil in a large Dutch oven over medium-high heat. Add the floured beef in a single layer and brown for 10 minutes, stirring occasionally, until all sides are well-caramelized. Remove beef and set aside.
Sauté Aromatics: To the same Dutch oven, add the diced yellow onion and sauté for 5 minutes, or until softened. Season with another pinch of salt and pepper.
Build the Sauce: Stir in the bay leaves, brown mustard, remaining flour, sliced mushrooms, and minced garlic. Cook for 1 minute, stirring constantly.
Simmer: Pour in the beef broth, scraping the bottom of the pot to loosen any browned bits. Bring the mixture to a boil, then reduce the heat to a simmer.
Tenderize: Return the browned beef to the Dutch oven. Cover and simmer for 1 hour, or until the beef is fork-tender.
Finish and Serve: Remove from heat and stir in the sour cream and butter until fully incorporated and melted. Serve hot over cooked egg noodles.