Preheat oven to 425°F.
Cut 2 medium Italian eggplants in half length-wise. Score the flesh by making shallow cuts in a diamond, or cross-hatch, pattern. Cover with 1/4 cup olive oil and 1/2 tsp salt and massage into the flesh and skin. Place the eggplant skin-side down on the baking sheet.
Peel and smash 4 garlic cloves and transfer them to the baking sheet along with 650-700g whole cherry tomatoes. Cover the tomatoes and garlic in 2 tbsp olive oil and 1/4 tsp salt. Toss to coat, then bake at 425°F for 35 minutes.
Meanwhile, in a small fry pan heat 2 tbsp olive oil on medium-low. Add 2 anchovy fillets and cook until the anchovy melts into the oil, about 2 minutes. Once melted, add 1/2 cup plain bread crumbs and increase heat to medium. Cook, while stirring frequently, until golden brown, about 5-10 minutes. Remove from heat and stir in 1/4 cup grated parmesan. It will clump at first, but just continue stirring, breaking up the chunks as you go. Season with a pinch of salt and freshly cracked black pepper. Taste and adjust. Set aside to cool.
After 35 minutes, the eggplant should be tender and tomatoes soft and jammy. Remove and flip the eggplant flesh-side up. Move the oven rack to the upper third and turn to broil.
Using a fork, place 6-8 cherry tomatoes and 1 garlic clove onto each half and smash lightly into the eggplant flesh. You don't want to leave any garlic on the pan because it will burn. Cover in fresh mozzarella and remaining parmesan. Place the eggplant under the broiler and cook until golden brown and bubbly, about 5 minutes.
Remove and top with toasted bread crumbs and fresh basil. Serve with remaining roasted tomatoes on the side.
