"Create a vegetable lasagna recipe using carrots, 3 Indian long eggplants, corn, a medium amount of cauliflower, a medium amount of broccoli, and a minimal amount of cabbage (about 1.5 cups). The vegetables should be cooked until very soft and smooth, with no crunchy texture in the finished lasagna. Make it a complete lasagna recipe with sauce, cheese, layering, and baking instructions. Emphasize techniques to soften the vegetables thoroughly before assembling."