Step 1

Heat 2 Tbsp. oil and 1 Tbsp. butter in a large skillet over medium-high until butter is melted. Cook mushrooms, tossing occasionally, until browned and tender, about 5 minutes. Season with salt, then transfer to a plate.

Step 2

Combine 1 Tbsp. oil and remaining 1 Tbsp. butter in same skillet. Season steak generously with salt and pepper. Cook until well browned, 3–4 minutes per side for medium-rare, depending on thickness. Transfer to another plate; wipe out skillet.

Step 3

Reduce heat to medium and pour remaining 1 Tbsp. oil into pan. Cook shallots, stirring often, until softened, about 2 minutes. Add garlic; cook, stirring, until softened, about 1 minute. Add tomato paste and cook, stirring constantly, until slightly darkened in color, about 2 minutes. Add flour and cook, stirring often to coat shallots and garlic, until toasty smelling, about 3 minutes. Add wine; cook, scraping up browned bits, until evaporated, about 1 minute. Add broth, fish sauce, and any liquid from mushrooms (leave mushrooms behind). Bring to a boil over high heat, then reduce heat; simmer, stirring occasionally, until sauce coats a spoon, 12–15 minutes.

Step 4

Slice steak against the grain. Place sour cream in a small heatproof bowl and gradually whisk in 1 cup sauce. Stir back into sauce in skillet. Taste and season with more salt or fish sauce if needed. Stir in mushrooms. Serve sauce over noodles, topped with steak and scallions.