In a bowl, combine the softened butter, miso paste, finely chopped shiitake mushrooms, chives, soy sauce, and lime juice. Mix until well combined and smooth.

Spoon the mixture onto a piece of plastic wrap, shape it into a log, and twist the ends to seal. Refrigerate for at least 30 minutes to firm up.

Preheat your grill or stovetop grill pan over medium-high heat.

In a small bowl, mix the chopped garlic scapes, lime zest, lime juice, olive oil, salt, and pepper. Rub the mixture evenly over each filet mignon steak.

Place the filet mignon on the grill and cook for about 4-5 minutes on each side for medium-rare, adjusting the time based on your preferred doneness.

Remove the steaks from the grill and let them rest for 5 minutes.

Slice the chilled miso-shiitake compound butter into rounds and place a slice on top of each filet mignon right before serving. Garnish with fresh cilantro and serve immediately.