How to Make It
Stir together oil, Worcestershire, tamari, lemon zest, thyme, Sriracha, and garlic in a medium bowl. Place steak in a 13- x 9-inch baking dish or a gallon-sized plastic ziplock bag; pour marinade over steak to fully coat. Cover, and let marinate at least 2 hours or up to overnight in refrigerator, turning occasionally.
Preheat broiler to HIGH with an oven rack 6 to 8 inches from heat. Line a large rimmed baking sheet with aluminum foil. Toss together potatoes, 1 tablespoon of the oil, 1 teaspoon of the salt, and 1/2 teaspoon of the pepper. Spread in an even layer on prepared baking sheet. Broil until starting to blister, about 5 minutes.
Remove steak from marinade. Pat dry; discard marinade. Place steak in center of prepared baking sheet, and arrange blistered potatoes around steak. Sprinkle steak with 1/4 teaspoon each of the salt and pepper. Broil 3 minutes.
Toss together broccoli, and remaining 2 tablespoons oil, 1/4 teaspoon salt, and 1/4 teaspoon pepper. Arrange broccoli around steak, and broil until potatoes are fork tender, broccoli is charred and tender, and a thermometer inserted into the thickest part of steak registers 125°F, 5 to 8 minutes. Let steak rest 10 minutes before thinly slicing against the grain.
While steak rests, prepare the aioli: Stir together mayonnaise, roasted garlic, lemon juice, salt, pepper, and sugar in a small bowl. Serve sliced London broil and vegetables with aioli.