Brush the zucchini, cabbage and radicchio with some olive oil and sprinkle with the basil. Season with salt and pepper. Add the veggies to the grill and cook until tender and grill marks appear, 10 to 20 minutes depending on the vegetable. Chop the grilled veggies lengthwise into thin strips.
In a small bowl, mix the olive oil, apple cider vinegar and agave. Season the vinaigrette with salt and pepper to taste. Toss the grilled veggies in the vinaigrette.