Preheat oven to 450°F.
For the salsa, blend all ingredients in food processor until almost smooth. Transfer to a bowl and set aside.
Season meat with salt and bring to room temp. Pat dry and season with graunlated onion, and garlic, and pepper.
Preheat a cast-iron skillet over medium-high to high heat.
Arrange broccolini on one end of a baking sheet and sprinkle with shallots. Arrange shishitos on the opposite end of the baking sheet and dress everything lightly with oil. Season with salt and pepper, and roast to tender-crisp and browned at edges.
Sear meat in hot skillet in a drizzle of oil for 6-7 minutes for medium-rare or 8-10 for medium. Remove steak to a cutting board and let rest 5-10 minutes. Place limes cut-side down in the hot pan to char. Remove and reserve.
While meat rests, in a nonstick pan over medium heat melt butter and cook eggs over easy to medium.
Slice steak against the grain. Douse meat and roast vegetables with juice from charred lime. Sprinkle meat and vegetables with Togarashi.
Fan meat on plates and top with egg or eggs and salsa verde. Serve the broccolini and roast shisitos alongside.