Position one oven rack to the lower-middle position and a second rack 8 inches from the broiler element. Heat the oven to 375°F. Line two rimmed baking sheets with parchment paper and spray generously with oil. Brush both sides of the eggplant slices with oil and season with salt and pepper. Arrange the slices in a single layer on the prepared sheets and bake until tender and lightly browned, about 30 to 35 minutes, switching and rotating the sheets halfway through. Let the eggplant cool for 5 minutes, then flip each slice over using a thin spatula.

Heat the remaining oil in a 12-inch broiler-safe skillet over medium-low heat until shimmering. Add the garlic, salt, oregano, and pepper flakes and cook, stirring occasionally, until fragrant. Stir in the tomatoes and their juice, increase the heat to high, and bring to a simmer. Reduce the heat back to medium-low and simmer until the sauce has thickened, about 15 minutes, then cover to keep warm.

Pulse the bread in a food processor until it forms fine crumbs. In a medium bowl, combine the bread crumbs, ricotta, a portion of the Pecorino, the larger portion of basil, lemon juice, and salt.

Spoon the ricotta mixture over the bottom third of each eggplant slice, using slightly more filling for larger slices. Gently roll the slices up and place them seam-side down into the tomato sauce in the skillet.

Heat the broiler. Bring the sauce to a simmer over medium heat on the stovetop for 5 minutes. Transfer the skillet to the oven and broil until the eggplant is well browned and the cheese is heated through, about 5 to 10 minutes. Remove from the oven and sprinkle with the remaining Pecorino. Let the dish stand for 5 minutes to set, then finish with the remaining basil and serve warm.