Add the olive oil and 1 tablespoon of butter to a large heavy-bottomed pan set over medium-high heat. Add the onions and cook, stirring frequently, until starting to soften ( approximately 2-3 minutes).
Add the ground beef to the onions and use a large wooden spoon or spatula to break the beef into smaller and smaller bits and pieces. Season with salt and pepper and continue to cook until ground beef is browned and cooked. Add the minced garlic to the beef and continue to cook for 1-2 minutes. Remove beef and onions from the pan and set aside. Drain excess fat from the pan.
Return pan to medium-high heat. Add 1 tablespoon of butter and add the sliced mushrooms in a single layer to the pan. Cook the mushrooms until nicely browned, approximately 4 minutes. Remove mushrooms to a clean plate and repeat until all mushrooms have been cooked.
Once all the mushrooms have been cooked, add them back to the pan and set over medium-high heat. Season with salt, pepper, and 1 teaspoon of paprika. Mix just to combine then immediately add 1/2 cup of dry sherry or white wine (or water) to deglaze the pan. Allow the liquid to reduce by half.
Add any remaining butter to the pan and sprinkle the mushrooms with 3 tablespoons all-purpose flour. Continue to cook, stirring continuously, 1 minute.
Still stirring continuously, slowly add the beef broth to the mushrooms. Once half the broth has been added, stir in the rest and mix well to combine. Add the beef back to the pan, mix well, and cook for 2-3 minutes, stirring occasionally.
Add the sour cream and bring just to a simmer. Reduce heat too low and continue to simmer for 4-5 minutes, stirring frequently. Do not boil.
Season with additional salt and pepper, to taste and season with fresh chopped parsley, if desired. Serve with egg noodles, pasta noodles, fresh bread, or mashed potatoes.