Step 1Coat the peppers with one-half teaspoon of olive oil. Roast on a baking pan, turning frequently until the peppers are vibrant in color with some char marks and the skin peels easily, about 35 minutes.
Step 2Remove the peppers from the oven and place them in a bowl. Cover the bowl tightly with plastic wrap. Let the peppers stand about 20 minutes or until cool. Peel the peppers, cut them into quarters and remove any seeds. Pat dry and cut into julienne strips.
Step 3Whisk the vinegar, garlic and shallot. Slowly whisk in 6 tablespoons of the olive oil. Add kosher salt and pepper to taste.
Step 4Pour the vinaigrette over the pepper strips and let stand while preparing the eggplant.
Step 5Cut both ends off the eggplant and slice crosswise into three-fourths-inch rounds and sprinkle with 1 teaspoon kosher salt. Brush both sides of the sliced eggplant lightly with 2 tablespoons of olive oil.
Step 6Grill the eggplant over medium heat. Cook until tender, about 8 to 10 minutes, turning once, until charred and softened. Remove from heat.
Step 7Arrange grilled eggplant on serving plates and spoon over marinated peppers. Garnish with torn basil. Season with fleur de sel and coarse cracked black pepper to taste.