Preheat the grill on medium-high heat and wash the vegetables under running water.
Cut the eggplant and the zucchini lengthwise, 1/4 to 1/2-inch think. Slice the onion the same fashion, but crosswise.
Remove the seeds and the white part of the bell pepper. Then, cut it into thin slices.
Cut the radicchio head into wedges, making sure the leaves are still attached to the core in each wedge.
Grill the vegetables without overlapping them, a few at a time if necessary. Cook for 4 to 5 minutes on each side until you can see some nice charred marks.
In the meantime, prepare the dressing. In a small bowl, combine extra virgin olive oil, balsamic vinegar, oregano, salt and pepper. Whisk everything together with a fast movement until all the ingredients are well combined.
Tear the basil leaves with your hands to release the aroma and add them to the bowl.
When the vegetables are ready, transfer to a serving plate and pour the dressing over them. Serve immediately.
