Place the eggs in a single layer in a medium pot, add enough water to cover by 1 inch and bring to a boil over high heat. Lower the heat to medium-low and simmer for 10 minutes. Transfer the eggs to a bowl of ice water. Peel them one at a time by filling a mason jar about 1/3 full with water, adding an egg, sealing the jar and shaking it until the shell is cracked. Remove the egg from the jar and carefully peel away the shell. Repeat with the remaining eggs.
Meanwhile, slice the steak into 1/4-inch-thick strips and season it with salt and pepper. Melt the butter in a medium skillet over medium-high heat. When the butter foams, add the steak and cook until cooked through and crispy on all sides. Remove the steak from the skillet and transfer to a cutting board. Cool and finely chop the steak.
Split the cooled eggs in half lengthwise using a damp cloth to wet your knife; clean the knife on the cloth after splitting each egg. Pop the yolks out into a medium bowl. Add the mayonnaise, mustard and a pinch of salt and pepper to the yolks and whisk until smooth. Taste and add more salt and pepper if needed.
Set aside 1 tablespoon of the steak for garnishing the eggs; fold the rest of the steak and the crabmeat into the yolk mixture. Fill a disposable piping bag with the yolk mixture and snip off the end to create a large hole. Pipe the filling evenly into each of the egg white halves. Sprinkle herbs and the reserved steak on top of the filled eggs and serve.