Melt butter and oil in a skillet over medium-high heat. Add mushrooms, season with salt, and saute, stirring occasionally, until they turn golden brown, 5 to 10 minutes.
Add onion and ground beef. Cook, stirring, until meat is browned and crumbly, and onions turn soft and translucent, about 5 minutes. Season with black pepper and cayenne.
Stir in minced garlic and flour, and cook for 1 minute.
Pour in vodka and allow to evaporate, about 30 seconds.
Stir in beef broth and water and bring to a simmer. Cook, stirring occasionally, for 10 minutes.
Reduce heat to medium, and mix in noodles. Cover with a tight-fitting lid and simmer for 5 minutes. Uncover and stir thoroughly. Cover again and cook until noodles are just tender, about 3 minutes. (See Cook's Note.)
Once noodles are cooked, reduce heat to low, and stir in sour cream.
Serve immediately with additional sour cream and green onions or chives if so desired.