Preheat griddle or grill pan or large cast-iron skillet over medium-high heat.
Preheat oven to 425°F and bring a 3-4 inches of water to a boil in large, deep skillet or pot.
For sauce, add vinegar and lemon juice to food processor then fill with parsley, anchovies, capers, pepper, red pepper, shallot and garlic. Pulse to fine chop then stream in olive oil. Process until fairly smooth.
Salt boiling water and cook rapini 3-4 minutes then cold shock in ice water bath. Pat the rapini dry on kitchen towels and place on large rimmed baking sheet. Dress the rapini with olive oil, season with salt, pepper and nutmeg, toss with red chili and garlic, and roast to tender and crispy at floret edges, 20-25 minutes, turning once.
Grill steak about 8 minutes turning once for medium-rare and let rest. Slice steak on an angle against the grain.
Divide rapini among dinner plates and top with sliced steak arranging slices perpendicular to greens and top with lemony salsa verde.