In a large skillet, melt the butter over medium heat. Add the chopped onion and garlic, cooking until they are tender and aromatic. Stir frequently to prevent them from browning or caramelizing.
Add the ground beef to the skillet with the onion and garlic. Cook it thoroughly, ensuring all of the meat is browned evenly. Use a wooden spoon to break it into small pieces to promote uniform cooking.
Once the beef is browned, incorporate the sliced mushrooms. Cook them together until the mushrooms are soft and have released their juices, adding a deeper flavor to the blend.
Sprinkle flour over the beef and mushroom mixture, stirring well to combine. Gradually add the beef broth, mixing until the sauce begins to thicken slightly.
Lower the heat, then carefully stir in the sour cream until the sauce is creamy and smooth. Season with salt, pepper, and paprika if desired. If the sauce becomes too thick, adjust its consistency with a bit more broth.
Notes
Store leftovers in the fridge for up to three days or freeze for up to two months. To reheat, gently warm on a stovetop or microwave.