No oven required: This simple one-pan lasagna cooks on the stovetop. Slideshow: More Lasagna Recipes
In a medium frying pan, heat the vegetable oil over medium high heat. Add the onion and cook for 5 minutes, until it is soft and starting to brown. Add the carrot, bell pepper and garlic and cook for 5 minutes. Stir in the marinara sauce and water. Remove all but 1/3 cup of the sauce from the pan; set aside.
In a medium bowl, whisk together the ricotta, egg, cream cheese, Dijon mustard, sea salt and freshly ground pepper.
Arrange half of the lasagna noodles in the sauce in the pan, breaking them so that they fit. Pour half of the remaining marinara sauce over the noodles, and spread with half of the ricotta. Arrange the rest of the noodles on top and cover with the remaining marinara sauce and ricotta. Sprinkle with the Parmigiano-Reggiano cheese. Bring the pan to a boil, cover it with aluminum foil, reduce the heat to low and simmer, covered, for 20 minutes.
Uncover the lasagna, spoon the pan juices over any noodles that are not in the liquid and continue to cook for 10 minutes, until the noodles are soft.