This is a version of lengua (beef tongue in a creamy mushroom sauce) from the Philippines, though this version uses beef sirloin since tongue isn't always easy to get everywhere. But both recipes tastes quite similar.
In a bowl, combine beef, salt and pepper. Massage seasonings onto meat and let stand for about 10 to 15 minutes.
In a wide pan over medium heat, heat oil. Add mushrooms and cook for about 30 seconds. Remove from pan and keep warm. Add beef in a single layer and sear for about 1 to 2 minutes per side or until lightly browned. Do not overcrowd pan, cook beef in batches as needed. Remove meat from pan and keep warm.
In another pan over medium heat, heat butter. When it begins to melt, add onions and garlic and cook, stirring regularly, until limp. Add flour and cook, stirring regularly, until lightly browned and begins to smell "nutty".
Add broth, whisking vigorously with a wire whisk until smooth and slightly thickened. Add beef. Season with salt and pepper to taste. Lower heat, cover and continue to cook for about 50 minutes to 1 hour or until beef is fork-tender. Stir occasionally and add more broth in ½ cup increments if sauce becomes too thick.
When meat is tender, add cream. Stir to disperse. Add mushrooms and continue to cook at low heat for about 2 to 3 minutes or until mushrooms are heated through.After the cream is added, make sure sauce does not boil to prevent the cream from separating. Serve hot.