For the London broil: Whisk together the molasses, vinegar, mustard, olive oil, rosemary, soy sauce and garlic in a 2-cup measuring cup. Pour the marinade into a 1-gallon ziptop bag, add the London broil and turn to coat with the marinade. Refrigerate for 4 hours (or at least 1 hour if time is limited). Remove the steak from the fridge at least 30 minutes before grilling to remove the chill.
Heat a cast-iron grill pan or outdoor grill on medium-high heat. Remove the London broil from the marinade, letting the excess drip off. Season the steak well with salt and pepper. Grill on each side for 10 to 12 minutes, a total of 24 minutes. Let rest for 10 minutes before slicing across the grain.
For the salad: Add the tomatoes, zucchini, red and yellow bell peppers and onions to a large rimmed baking sheet and add the olive oil. Sprinkle evenly with salt and pepper, tossing to coat all the veggies in the oil. Place in a grill basket and grill over medium high until tender and lightly charred, about 5 minutes per side. (If using an indoor grill pan, you will need to grill in 2 batches to avoid overcrowding the pan and steaming the veggies.)
Remove the charred vegetables to a cutting board and let rest until cool enough to handle. Chop into bite-size pieces. Add the chopped vegetables, basil and arugula to a large bowl. Drizzle with the balsamic and a small drizzle of olive oil, season with some salt and pepper and toss it all together. Serve with the sliced steak.