Preheat oven to 425˚F.
Boil the lasagna noodles for 7 minutes.
Meanwhile, heat a large skillet over medium heat and add the olive oil and butter. Toss in the onions and cook for 2 minutes.
Add the garlic and cook for 20 seconds.
Stir in the carrots and zucchini, and season with salt and pepper. Continue to cook, stirring occasionally, for 7 to 8 minutes, or until the vegetables are slightly tender.
Drain the cooked lasagna noodles and layer them on top of the vegetables in the skillet.
Top the noodles with the diced tomatoes and stir in the chopped basil.
Remove the skillet from the heat and bake in the oven for 10 minutes.
Remove from oven; top with grated parmesan cheese, if using, and serve.