Heat a grill or grill pan on medium-high heat.
Add the tomatoes, zucchini, red and yellow bell peppers and onions to a large rimmed baking sheet and drizzle liberally with 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 until tender and lightly charred, about 5 minutes per side. If using an indoor grill pan, you will need to grill in two batches to avoid overcrowding the pan and steaming the veggies.
Remove the charred vegetables to a cutting board and rest until cool enough to handle. Chop into bite-size pieces. Add the chopped vegetables, arugula and basil 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.