Preheat the oven to 350 degrees. Shuck the corn (remove the husks - the papery outer layer) and use a knife to cut off the kernels. Chop the fresh tomatoes into 1-inch pieces, removing seeds. Coat the corn, tomatoes, and garlic with olive oil and season with salt and pepper. Do not peel the garlic before roasting. Roast the vegetables on rimmed baking sheets for 30 minutes. Use a spatula to stir every 10 minutes, scraping up any bits that are sticking.
While the vegetables are roasting, prepare the tomato sauce. Peel the onion and cut into halves. Combine the canned tomatoes, butter, and onion halves in a saucepan. Bring to a simmer, then cook for 45 minutes, stirring occasionally. (This sauce was created by Marcella Hazan's)
Remove the corn from the oven and transfer half of the kernels to a food processor. Peel the roasted garlic (carefully - it will be hot, so you may need a fork and knife) and add it to the food processor. Blend until the corn forms a rough paste. Allow to cool about 5-10 minutes (until the corn stops steaming). Add the solid burrata cheese and blend until smooth. Use some of the liquid from the burrata container to thin the cheese-corn mixture if it is thick. It should be smooth and spreadable.
Assemble the lasagna: Start with a layer of roasted tomatoes, basil, and tomato sauce on the bottom of the pan, add a layer of lasagna noodles (either fresh, precooked dry pasta, or no-boil noodles), and finish with the burrata-corn mixture. Sprinkle half of the remaining whole roasted corn kernels over the burrata. Add another layer of pasta sheets and repeat the process. The lasagna should have 2 tomato layers and 2 burrata-corn layers. Spread the top layer of lasagna noodles with any remaining tomato sauce and sprinkle with shredded mozzarella cheese. Cover with tinfoil and bake 30 minutes, rotating every 10 minutes. Turn the heat up to 400 degrees, remove the foil, and bake a final 10 minutes. Allow to cool slightly but serve hot.