For the beet creme fraiche: Combine the beet juice and sugar in a small nonreactive saucepan and bring to a boil over high heat. Cook until thickened and reduced to about 1/4 cup, about 30 minutes. Transfer to a bowl and refrigerate until cold, about 30 minutes.
Place the creme fraiche in a bowl, season with salt and pepper and swirl the beet reduction into the creme fraiche.
For the buttered noodles: Bring a large pot of salted water to a boil, add the noodles and cook until al dente, about 6 minutes. Drain the noodles, reserving 1 cup of the cooking water.
Melt the butter in a large saute pan, add the noodles and some of the cooking liquid and toss to coat. Stir in the dill and parsley and season with salt and pepper.
For the stroganoff: Season both sides of the beef with salt and pepper and then the steak rub. Heat 3 tablespoons of the oil in a large saute pan over high heat until it begins to shimmer. Add the beef and cook on both sides until golden brown, a crust has formed and the meat is cooked to medium rare, about 10 minutes. Remove to a plate and let rest for 5 minutes. Slice into 1/2-inch thick slices.
Add the butter and remaining tablespoon of oil to the pan and heat until it begins to shimmer. Add the mushrooms and cook until lightly golden brown. Add the shallots and garlic and continue cooking until soft, the mushrooms are deep golden brown and the liquid has evaporated, about 5 minutes per side. Season with salt and pepper. Stir in the flour and cook for 1 minute. Add the beef stock, bring it to a boil and cook until the sauce coats the back of a spoon, about 10 minutes.
To serve: Put some of the noodles in each bowl. Top with the mushrooms, sliced steak and a dollop of the beet creme fraiche. Garnish with parsley leaves and dill.