In a mixing bowl, combine the softened butter, miso paste, grated ginger, lemon juice, and a pinch of salt. Mix until smooth and well combined.

Place the mixture on a piece of plastic wrap, roll it into a log shape, and twist the ends to seal. Refrigerate while preparing the steaks.

Preheat your grill or a skillet over medium-high heat. Rub the filet mignon steaks with olive oil, and season generously with salt and pepper on both sides.

Place the trimmed scallions directly on the grill or in the skillet. Grill for about 2-3 minutes, turning occasionally until they are charred and tender. Remove and set aside.

Add the seasoned filet mignon steaks to the grill or skillet. Cook for about 4-5 minutes per side for medium-rare, or until your desired doneness is reached.

During the last minute of cooking, sprinkle the lemon zest, chopped parsley, and thyme leaves over the steaks.

Transfer the cooked steaks to a plate and let them rest for about 5 minutes. Slice the charred scallions and arrange them alongside the steaks.

Slice the compound butter and place a piece on top of each steak just before serving.