Finely chop leftover meat until it becomes minced and tender. Add butter to a hot skillet. Whisk eggs and spread in a thin layer. Add minced meat to the center with grated cheese, chopped chives and any leftover sauce you want to include. Season with salt and pepper.
Fold eggs in on each side, left, right, top and bottom until all the fillings are packaged neatly in the eggs. Cook for another 2-3 min on medium to low heat until cheese melts and eggs are cooked through.
Toast brioche bun and spread some dijon mustard on each slice. Add eggs and arugula and close sandwich. Slice in half and enjoy!
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Notes
Note: I also added some leftover sauce and shallots that the beef was cooked with. I encourage you to do the same if you have it!