Step 1

Preheat broiler on high with a rack 8 inches below element. Combine panko, cheese, and lemon zest; season with salt and pepper. Stir in 2 tablespoons oil to evenly coat. On a rimmed baking sheet, brush eggplant evenly with 2 tablespoons oil; season.

Step 2

Broil, flipping once, until eggplant is tender and golden brown on both sides, about 10 minutes a side. Top evenly with panko mixture (about 1/3 cup on each plank) and broil until panko turns crisp and golden brown, 2 to 3 minutes.

Step 3

In a large bowl, whisk together lemon juice, paprika, and remaining 1/4 cup oil; stir in mint and season. Drizzle about half of dressing over eggplant. Squeeze tomatoes over bowl to release juices, then drop them into dressing and toss with arugula to evenly coat. Serve over eggplant, sprinkled with more paprika.