Preheat your broiler to high. Place the corn on a baking sheet and roast under the broiler, turning every couple of minutes, until all sides are browned and even a little charred, about 6 to 8 minutes. Let the corn cool and then hold it by one end and slice down the cob with a knife to separate the kernels from the cob.
Place the corn, tomatoes, parsley, and hearts of palm in a large bowl. Drizzle with some olive oil and season with salt and pepper and toss together. Scoop the salad into the radicchio cups and serve with lime wedges