Place an oven rack in the center of the oven. Preheat the oven to 200 degrees F.
For the vegetables: Place a grill pan over medium-high heat, or preheat a gas or charcoal grill. Drizzle the vegetables with olive oil and season with salt and pepper. Grill the eggplant until tender, about 4 minutes each side. Grill the asparagus for 3 to 4 minutes, turning occasionally until crisp-tender. When cool enough to handle, cut the asparagus in half crosswise.
For the filling: In a small bowl, mix together the ricotta cheese, basil, Pecorino Romano, lemon zest, and lemon juice until smooth. Season with salt and pepper, to taste.
To assemble: Place 4 slices eggplant on a work surface. Spread each with 2 to 3 tablespoons of the ricotta mixture. Line 4 pieces of asparagus, side-by-side, on top. Place another slice of eggplant on top and repeat the layers. Top each napoleon with a slice of eggplant and place on a small baking sheet. Bake until warmed through, about 10 minutes, and serve.
If the eggplant slices dry out in the oven, drizzle with olive oil before serving.
Recipe courtesy of Giada De Laurentiis