Preheat oven to 375 degrees F.
In a saute pan over medium heat, add extra-virgin olive oil. When almost smoking, add the onion and cook until soft, about 5 minutes. Add the carrot and cook for 3 minutes. Add the zucchini and squash cook for 5 minutes. Add asparagus and cook for 2 minutes. Remove from heat when all vegetables are completely cooked but still have a good crunch. Allow to cool.
Using a 6-inch round cookie cutter, cut circles out of the lasagna sheets. You will need 18 circles. Coat the bottom of 6 (6-inch) gratin dishes with a teaspoon of tomato sauce in each. Place a circle of pasta on the bottom of each ramekin. Rinse the beans with water and season with salt and pepper. Divide the beans between each ramekin. Next, divide the spinach between the ramekins. Place a second layer of pasta on top and gently press down. Divide the sauteed vegetables among the ramekins and top with a tablespoon of tomato sauce in each. Place the third layer of pasta in each ramekin and coat with a tablespoon of tomato sauce. Sprinkle ramekins with the mozzarella and Parmesan cheeses, and top each with 1/2 tablespoon of butter. Line a baking sheet with aluminum foil and place gratin dishes on top. Bake in oven for 20 minutes or until brown and bubbling.
For the tomato sauce:.
In a large casserole pot or Dutch over, heat oil over medium high heat. Add onion and garlic and saute until soft and translucent, about 5 to 10 minutes. Add celery and carrots and season with salt and pepper. Saute until all the vegetables are soft, about 5 to 10 minutes. Add tomatoes and bay leaves and simmer uncovered on low heat for 1 hour or until thick. Remove bay leaves and check for seasoning. If sauce still tastes acidic, add unsalted butter, 1 tablespoon at a time to round out the flavors.
Add 1/2 the tomato sauce into the bowl of a food processor. Process until smooth. Continue with remaining tomato sauce.
If not using all the sauce, allow it to cool completely and pour 1 to 2 cup portions into freezer plastic bags. This will freeze up to 6 months.