Cut the corn kernels from the cobs -- you should get about 8 cups. Reserve 1 cup, then place the other 7 cups in a blender and purée until smooth.
Combine the puréed corn with the remaining cup of reserved kernels in a medium saucepan with butter. Season with salt and pepper. Simmer polenta over medium heat until it's thick and the corn kernels are tender, 6 to 8 minutes.
While the polenta cooks, toss together tomatoes and the basil in a medium bowl, then season with salt and pepper. Pit and peel the avocados, then cut them into quarters. Divide the polenta among four serving bowls and top with avocado and tomato salad. Drizzle each serving with oil and vinegar.
Before her diagnosis, Caroline wrote a book on cakes called Cake Magic!. She started developing a birthday cake using her gluten-free mix found in that book. Check out other recipes she’s developing for her new life—and the stories behind them—on her blog, The Wright Recipes. Her next book, Catalan Food, written with chef Daniel Olivella, comes out in early September from Clarkson Potter.