Heat a large skillet over medium-high heat. Add steak. Cook and stir until steak is firm, hot in the center, and just turning from pink to grey, about 7 minutes. Transfer steak to a bowl.
Bring a large pot of lightly salted water to a boil; cook the rotini at a boil until tender yet firm to the bite, about 8 minutes; drain.
Melt 1 tablespoon butter and olive oil in the same skillet over medium-high heat. Saute onion and garlic until onion is tender, about 2 minutes. Add the cooked steak and mushrooms; cook and stir until mushrooms are tender and onions are translucent, 3 to 5 minutes.
Transfer beef mixture to a large pot over medium-low heat. Add water, beef base, and dill. Combine thoroughly and let soup simmer until roux is ready.
Melt 1/2 cup butter in the skillet. Whisk in flour until smooth. Cook, stirring constantly, until a thick roux is formed, about 2 minutes. Mix roux slowly and thoroughly into the soup, stirring constantly. Mix in the cooked pasta. Stir in cognac and remove from heat. Add sour cream and mix thoroughly. Top with parsley.