Sear the Beef: In a bowl, season the sliced beef with ½ teaspoon salt and ½ teaspoon pepper. Toss with 1 tablespoon flour to lightly coat. Heat 2 tablespoons oil in a large, deep skillet over medium-high until shimmering. Add beef in a single layer (work in batches if needed, adding oil as necessary). Cook 2–3 minutes per side, undisturbed, until browned but still pink inside. Transfer to a clean bowl.
Cook the Vegetables: In the same skillet, add the mushrooms (8 ounces) and onions (1/2 cup), along with 1–2 tablespoons of oil if the pan seems dry. Sauté, stirring often, until the mushrooms are golden and the onions have softened, 6–7 minutes. Add the garlic (3 cloves) and cook just until fragrant, about 1 minute. Adjust the heat as needed to keep the fond from burning — it’s the foundation of your flavor. Transfer the vegetables to the bowl with the beef.
Make the Roux: Lower the heat to medium. Melt butter (3 tablespoons) in the skillet, then whisk in the remaining flour to form a roux. Cook 1–2 minutes, whisking constantly, until nutty and golden. Watching again so the fond doesn't burn, stir in tomato paste (1 tablespoon) and cook 30–60 seconds.
Build the Sauce: Gradually whisk in 1–1 1/2 cups broth until the mixture is smooth and the lumps are dissolved. Add remaining broth, whisking until slightly thickened. Stir in beef bouillon (watching to be sure it dissolves) (1 teaspoon), sherry (2 tablespoons), Worcestershire (1 tablespoon), Dijon (2 teaspoons), thyme (1 teaspoon), tarragon (1/2 teaspoon), sugar (1/4 teaspoon), and remaining 1 teaspoon salt + ½ teaspoon pepper. Bring to a gentle boil.
Cook the Noodles: Stir in egg noodles (6 ounces), pressing them into the liquid so they’re mostly submerged. Reduce heat to medium-low and simmer, stirring often so noodles don’t stick, 5–6 minutes until almost al dente. Add a splash more broth if needed.
Finish the Sauce: Stir in sour cream (1/2 cup) and cream cheese (4 ounces) until smooth and silky. Taste and adjust seasoning.
Bring it All Together: Return beef, mushrooms, and onions (with any juices) to the skillet. Stir gently and cook 1–2 minutes until warmed through.
Serve: Garnish with parsley and serve hot, straight from the pan.