Preheat the broiler. In a skillet, heat 3 tbsp. EVOO over medium heat. Add the garlic and cook until golden, about 2 minutes; using a slotted spoon, transfer to a small bowl. Add the tomatoes to the pan; season with salt and pepper. Cook, undisturbed, until tender on one side, about 5 minutes. Stir and continue to cook, stirring occasionally, for about 5 minutes.
Line a baking sheet with foil; transfer the eggplant to the baking sheet in a single layer. Brush the eggplant on both sides with the remaining 3 tbsp. EVOO; season with salt and pepper. Broil, turning once, until tender and browned, about 8 minutes.
On the baking sheet, divide the eggplant into 4 portions. Spoon the tomatoes on top and cover with the cod. Broil until the fish is just cooked through, about 5 minutes. Using a wide spatula, transfer to plates. Top with the basil and garlic.