Trim off any stems or blemishes on the skin of the eggplants. Cut eggplants crosswise into slices about 3/8-inch thick.
Turn on broiler to heat. Place slices on a baking sheet and spray with oil, using a “ mister” if you have one. If not, lightly brush each slice with olive oil.
Place baking sheets under the broiler on the second shelf from the top, so that they are not too close, or they will burn.
When one side is slightly browned and soft when you press lightly, turn slices over, apply olive oil and return to broiler. Depending on your broiler, the distance from the pan, it may take 20 to 25 minutes to cook. (You may find that slices that are directly under the broiler cook much faster than those at the far corners of the pan. Keep a close eye on the pans and rotate the slices on the cookie sheet.)
Remove slices individually as they are done cooking and place on a large platter or serving plate. Don’t be afraid to overlap slices on the serving plate. It works just fine for serving and will be more appetizing.
While the eggplant is broiling, finely chop the tomatoes and place them into a medium size mixing bowl. Finely chop the green onions and put the garlic cloves through a press or mince them by hand and place in the bowl with tomatoes.
Remove the capers from the jar with a slotted spoon, so that they drain.
Chop the capers and mix into the bowl with other ingredients. Make sure that stems are removed from the basil leaves, then chop the basil and place in a bowl.
Pour olive oil and vinegar into the bowl and mix with the other ingredients.