Preheat the BBQ to medium-high heat for direct grilling.
Slice the eggplant into about 3/8 inch (1cm) slices. Not too thin or they will get mushy when you grill them.
Coat the red pepper all over with olive oil then place directly over the direct heat grill. Cook to get a good black char all over, turning the pepper over the grill as needed. Once well charred, place the bell pepper in a bowl covered with plastic wrap or in a resealable type plastic bag. Let the pepper steam for about 30 minutes. Remove the charred skin and slice lengthwise into 1/4 inch (6mm) strips. Set aside.
Sprinkle the salt evenly over both sides of the eggplant to help remove some of the bitterness and draw out some of the moisture. Let sit for 10 or 15 minutes, shake off any excess salt, then pat dry with paper towel.
Brush the oil on the eggplant. Place over the direct heat and grill each side until you have nice color, 5 or 6 minutes per side.
To assemble start with a base of eggplant then add about 1 tablespoon of goat cheese, 2 strips of bell pepper, then drizzle with the balsamic reduction and garnish with a basil leaf. Serve immediately.