1. Season steak with salt and pepper to taste. In a large pot, heat 1 tbsp (15 mL) of the oil over high heat. Add steak, in two or three batches, and sauté until just browned but still rare inside, about 1 minute per side, adding oil as needed between batches. Remove with a slotted spoon to a warm plate. Set aside and keep warm.
2. Reduce heat to medium, add 3 tbsp (45 mL) of the butter to the pot and heat until melted. Add shallots and sauté until softened, about 3 minutes. Add mushrooms and sauté until they have released their liquid and are browned, about 10 minutes. Sprinkle with flour and sauté for 2 minutes.
3. Gradually whisk in stock, then Cognac; bring to a boil. Reduce heat and simmer, stirring often, until soup is slightly thickened and flavors have blended, about 15 minutes. Gradually whisk in cream and mustard; simmer for 5 minutes. Do not let boil.
4. Meanwhile, in a large pot of boiling salted water, cook noodles until tender to the bite, 6 to 8 minutes. Drain, transfer to a bowl, add the remaining butter and toss to coat. Season with salt and pepper to taste. Keep warm.
5. In a bowl, whisk together sour cream and dill.
6. Divide beef and noodles among heated bowls and top with soup. Top each with a dollop of dilled sour cream.