Using fork, poke each piece of steak 10-12 times. Place in baking dish; rub both sides evenly with soy sauce. Cover with plastic wrap and refrigerate at least 15 minutes or up to 1 hour.
While meat marinates, place mushrooms in medium microwave-safe bowl and cover with plastic wrap. Microwave on high power until mushrooms have decreased by volume by half, 4-5 minutes (should be as much as 1/4 cup liquid in bowl). Drain mushrooms and set aside; discard liquid. Combine water, dry mustard, sugar, and 1/2 tsp pepper in a small bowl until smooth paste forms; set aside.
Pat steak pieces dry with paper towels and season with pepper. Heat oil in 12" skillet over medium-high heat until just smoking. Place steak pieces in skillet and cook until browned on all sides and internal temperature registers 125 to 130 degrees, 6-9 minutes, reducing heat if fond begins to burn. Transfer meat to large plate and set aside while cooking sauce.
Add mushrooms, onion, and 1/2 tsp salt to skillet and cook until vegetables begin to brown and dark bits form on bottom of pan, 6-8 minutes. Add tomato paste and flour and cook, stirring constantly, until onions and mushrooms are coated, about 1 minute. Stir in 1/3 cup wine, beef broth and mustard paste and bring to simmer, scraping bottom of pan with wooden pan to loosen browned bits. Reduce heat to medium and cook until sauce has reduced slightly and begun to thicken, 4-6 minutes.
While sauce is reducing, cut steak pieces across grain into 1/4" thick slices. Stir in meat and any accumulated juices into thickened sauce and cook until beef has warmed through, 1-2 minutes. Remove pan from heat and let any bubbles subside. Stir in sour cream and remaining tablespoons wine; season to taste with salt and pepper. Sprinkle with parsley.