Preheat the oven to 350 degrees F.
In a medium saucepan over medium-high heat, add the olive oil. Add the onions and cook until softened, about 3 minutes. Add the garlic and cook for another minute. Stir in the crushed tomatoes and bring to a simmer. Let simmer for 10 minutes. Remove from the heat and stir in the chopped basil.
In a medium bowl, stir together the ricotta with 1/4 cup of mozzarella cheese.
Lay out the grilled eggplant strips and put about 2 tablespoons of filling onto the bottom strips. Roll
Spread 1 cup of the tomato sauce onto the bottom of a small baking dish. Put the eggplant rolls, seam side down, into the baking dish. Cover the rolls completely with another cup of sauce and sprinkle with the remaining 1/4 cup of mozzarella. Bake in oven until the cheese is melted and bubbly, about 25 minutes.