Heat the olive oil over medium low heat. Add the onion and cook until softened, transparent, and lightly golden around the edges, about 10 to 14 minutes, stirring every few minutes. Add the garlic and saute until garlic is softened, another 3 to 5 minutes. Remove from heat and allow to cool for 5 minutes.
In a medium bowl, stir together the ricotta, cottage cheese, parmesan, egg, basil, thyme, fennel, salt, pepper, and sautéed onion mixture.
Preheat the oven to 375 degrees Fahrenheit. Bring a large pot of lightly salted water to a boil and cook the lasagna noodles until flexible, about 8 minutes. Drain the noddles and rinse them with cold water. Need 4 per layer, so 12 noodles total.
Spread 1 1/2 cups of the Bertolli® Rustic Cut Sweet Peppers and Portobello Mushroom sauce on the bottom of a greased 14 by 10-inch and 3-inch deep casserole dish. Arrange 4 noodles lengthwise in a single even layer over the sauce. Spread with 2 cups of the ricotta mixture, then place some of the bell pepper pieces on top in 2 side-by-side rows of 10, then spoon and spread 2 cups of the Bertolli® Rustic Cut Sweet Peppers and Portobello Mushroom sauce over the pepper layer. Repeat the process twice more starting with the layer of cooked noodles, so that at the end you have three different noodle layers and a layer of sauce on top.
Arrange the sliced tomatoes, cherry tomatoes, remaining bell pepper pieces, burrata, and mozzarella over the top of the lasagna. Place the dish on a lipped baking sheet and bake in the oven until the sauce is bubbling around the side, the fresh tomatoes on top are slightly wrinkled and darkened, and the cheese is completely melted, about 60 minutes to 1 hour 10 minutes.
Remove from the oven and allow to cool for 20 minutes before garnishing with the remaining 1/4 cup fresh basil leaves and serving.