How to Make It
Preheat grill to medium (350°F to 400°F) and lightly oil grates. Brush eggplants and bread on both sides with 3 tablespoons oil; set bread aside. Season eggplants on both sides with 1 teaspoon salt. Grill eggplants, uncovered, flipping once, until soft and grill marks appear, about 4 minutes per side. Transfer to a cutting board; let cool completely, about 15 minutes. Cut into ¾-inch pieces.
While eggplants cool, grill bread, uncovered, flipping once, until grill marks appear, 3 to 4 minutes per side. Transfer to a cutting board; let cool for about 10 minutes. Cut into 1-inch chunks.
Whisk lemon juice, mustard, and ¼ teaspoon salt in a small bowl. Gradually whisk in remaining 6 tablespoons oil.
Place eggplants, bread, kale, tomatoes, dill, and remaining ¼ teaspoon salt in a large bowl; add dressing and toss to coat. Top with cheese and serve.