Lay the steak flat on a board; tie kitchen twine tightly around the sides (including the bone) to help the steak keep its shape during cooking.
Grind the mushrooms in a spice grinder or blender; transfer to a bowl and mix with the garlic, balsamic vinegar, brown sugar, 1 tablespoon Worcestershire sauce, 1 1/2 tablespoons rosemary, the red pepper flakes and 2 teaspoons salt. Cut 8 deep slits about 1 inch apart all over the steak; fill each slit with some of the mushroom mixture, then rub the rest all over the meat. Transfer the steak to a plate, cover with plastic wrap and refrigerate 2 to 4 hours. Remove from the refrigerator about 1 hour before grilling.
Meanwhile, combine the butter, scallions, parsley, the remaining 1 tablespoon Worcestershire sauce and 1/2 tablespoon rosemary, and 1 teaspoon salt in a bowl. Cover and refrigerate until ready to use.
Preheat a grill to medium high, then prepare for indirect heat: For gas, turn off the burners on one side. For charcoal, push the coals to one side. Brush the steak with the olive oil, then place on the cooler side of the grill (indirect heat). Cover and cook, turning occasionally, until a thermometer inserted into the thickest part registers 110 degrees F to 120 degrees F, 20 to 30 minutes. Move the steak to the hotter side of the grill (direct heat) and cook until the thermometer registers 125 degrees F, 2 to 3 more minutes per side. Transfer to a cutting board and let rest 15 minutes, spreading with some of the herb butter.
Meanwhile, grill the peppers over direct heat, turning, brushing with the lemon juice and seasoning with salt, until charred, 8 to 10 minutes. Top the steak with more herb butter and serve with the peppers.