Step 1

Serve with pasta.

Step 2

Sprinkle eggplant slices all over with 1 teaspoon salt and let sit for 15 minutes. Cook panko, 2 tablespoons oil, and pinch salt in 12-inch skillet over medium heat, stirring often, until golden brown, 3 to 6 minutes. Transfer to bowl and wipe skillet clean with paper towels.

Step 3

Cook 2 tablespoons oil and garlic in now-empty skillet over medium-high heat, stirring often, until fragrant, about 1 minute. Stir in tomatoes; reduce heat to medium-low; and cook until slightly thickened, about 5 minutes. Off heat, stir in Parmesan, 
2 tablespoons parsley, sugar, 
and remaining ½ teaspoon salt. Cover to keep warm.

Step 4

Brush eggplant all over with remaining 3 tablespoons oil. Grill eggplant over hot fire until charred, 3 to 5 minutes. Flip eggplant. Spread about 1 tablespoon sauce over each eggplant slice, then sprinkle mozzarella evenly over top. Grill until eggplant is tender and cheese is melted, 3 to 5 minutes. Transfer 
eggplant to serving platter and sprinkle with panko and remaining 
2 tablespoons parsley. Serve, passing remaining sauce separately.