Mix the butter, chives, tarragon, and garlic together in a bowl until well-blended.
Place the butter mixture on a large piece of plastic wrap. Wrap the butter with the plastic and shape it into a log about 1-inch thick.
Place the log in the refrigerator to chill.
Season the beef tenderloin steaks with salt and black pepper.
Place the dried mushrooms in a spice grinder or food processor. Process until the mushrooms are finely ground.
Spread some of the ground mushroom on a plate. Press each steak into the mushroom powder until well coated, adding more mushroom to the plate as necessary.
Melt about 2 tablespoons herb butter in a large skillet over medium heat. Arrange the steaks in the skillet and cook until they start to firm, and are reddish-pink and juicy in the center, about 6 minutes per side. An instant-read thermometer inserted into the center should read 130 degrees F (54 degrees C) for medium rare, 140 degrees F (60 degrees C) for medium. Top each steak with 1 teaspoon herb butter before serving.