Step 1

Fresh Tomato Sauce: Heat oil in a medium straight-sided skillet over medium. Add garlic; cook until fragrant, about 30 seconds. Stir in tomatoes, 2 teaspoons salt, and 1/2 teaspoon pepper. Cook, stirring occasionally and breaking up tomato pieces with a wooden spoon, until tomatoes are soft, about 10 minutes. Remove from heat; let stand 10 minutes. Pass through the medium disk of a food mill. Sauce can be allowed to cool completely, then refrigerated in an airtight container up to 5 days. (Makes about 2 1/2 cups.)

Step 2

Involtini: Trim and cut eggplants length-wise into 1/4-to-1/2-inch-thick slices. Place on a rimmed baking sheet fitted with a wire rack; season both sides with salt. Let stand 30 minutes.

Step 3

Meanwhile, preheat oven to 375°F. Place currants in a small heatproof bowl and cover with boiling water. Let stand 10 minutes, then drain. Finely chop half of mozzarella and place in a bowl with currants, ricotta, feta, pine nuts, cinnamon, oregano, parsley, breadcrumbs, and egg. Season with salt and pepper; stir to combine.

Step 4

Heat a grill or grill pan to medium-high. Pat eggplant slices dry with paper towels and brush both sides of each evenly with olive oil. Brush grates with vegetable oil and grill eggplant slices, turning occasionally, until charred in places and tender, about 3 minutes a side.

Step 5

Transfer to a plate, piling slices on top of one another so that they continue to steam and soften. Let cool 15 minutes. Place 1 to 2 tablespoons filling at one short end of an eggplant slice. Roll up tightly to secure in a cigar shape. Repeat with remaining filling and eggplant slices.

Step 6

Spread tomato sauce evenly in the bottom of a 9-by-12-inch gratin dish or 9-inch square baking dish. Arrange eggplant rolls snugly in an even layer, seam-sides down. Thinly slice remaining mozzarella and arrange over top.

Step 7

Drizzle with olive oil and sprinkle with pepper. Bake until cheese has melted and eggplant is bubbly, about 30 minutes. Let cool slightly, then garnish with basil and serve with bread.