Cut meat into 1/2-in. cubes and pat dry. In a medium bowl, whisk together flour, 1 tsp. salt, and 1/2 tsp. pepper. Add meat to bowl and toss to coat; then lift out, shaking off any excess flour.
Chop 4 chives and set aside. Cut remaining chives into 1-in. pieces and set aside.
Heat a wide 6-qt. pot over medium-high heat for 2 minutes. Swirl in 2 tbsp. oil. Add half of meat in a single layer and cook, without moving, until browned. Turn meat and brown on all sides, 6 to 8 minutes, then transfer to a plate. Swirl 2 more tbsp. oil into pot, add rest of meat, and brown the same way.
Pour remaining 1 tbsp. oil into pot. Add mushrooms, shallots, garlic, and remaining 1/2 tsp. salt and cook, stirring, until mushrooms release their liquid, about 5 minutes. Add wine and simmer until liquid is reduced by half, about 5 minutes. Add stock and bring to a boil; then reduce heat to medium and simmer, stirring occasionally, until the liquid is reduced by half, about 25 minutes.
Meanwhile, bring a large pot of water to a boil. Add enough salt to make the water as salty as the ocean. Add noodles and cook until tender. Reserve 1/2 cup cooking water, then drain noodles.
Add sour cream, mustard, and browned tenderloin to mushrooms and reduced stock and simmer about 2 minutes for medium rare. Season with salt and pepper. Add noodles and toss gently but thoroughly to coat. Toss with chopped chives and some reserved cooking water to loosen sauce, if necessary.
Serve in wide, shallow bowls, each serving topped with crème fraîche if you like and a couple of chive pieces.
*Order elk online from montanaelk.com.