Mix the olive oil, garlic, salt, pepper and 1/2 teaspoon of the basil together.
Slice the eggplants lengthwise into 1/2" slices. Brush the slices on both sides with the olive oil mixture.
Grill the eggplant slices until they become soft in the center, about 2 to 3 minutes on each side.
For the wraps: Mix the cheese, the remaining teaspoon of basil, salt and pepper together. Set aside.
Spread the tortillas out on a work surface in front of you. Spread the cheese mixture out on the tortillas, then top with the spinach or arugula, a slice of tomato and a few slices of eggplant. Tightly roll the tortillas into a cylinder, ending with the seam side down.