Begin by making the dressing. Bring a medium pot of water to a boil and blach the basil in the water for 30 seconds & drain. Then squeeze to remove as much of the water as possible. Add it to a small food processor or a large measuring cup (if using an immersion blender.) Add the 1/4 cup oil and the rest of the dressing ingredients. Puree until smooth & taste for salt & pepper. Set aside.
Drizzle both sides of the chicken breasts with 1 tbsp olive oil and season with salt & pepper. Grill using your method of choice, about 6-7 minutes per side. (don't move the chicken once you put it down to get those nice grill marks. Set the chicken on a plate.
Brush the grill or grill pan with the rest of the olive oil, using a little more if necessary so nothing sticks. Place the corn cobbs and carefully lay the peach wedages on the grill. Grill the corn on all sides and just a couple minutes on each side for the peaches to get slightly charred but to still retain a little bite. Set all aside when done.
Once the corn is cool enough to handle, carefully slice the kernels off. Then slice the chicken breasts.
To assemble, you can either make one big platter or small individual salads. First arrange the arugula on the plate, drizzle with a small amount of dressing and toss a bit. Then sprinkle the corn all over, followed by the tomatoes, chicken slices, the peaches and tuck the fresh basil leaves throughout. Drizzles on a little more dressing, reserving some on the side for everyone to add as they wish. Season with salt & pepper if needed. Enjoy!
*If making to enjoy for dinner for two nights. Assemble individual portions and store all the components separately in the refrigerator. Pull out the dressing about 30 minutes to an hour before serving.