Shear the corn kernels from the cobs with a knife, working over a large bowl or tube pan to catch the kernels. Run a knife along the cobs to press out the milky juices and add to the kernels. Break 4 cobs in half and combine with the half-and-half and 1 cup water in a saucepan. Discard the remaining cobs or save for making a broth. Bring to a simmer over medium heat, cover and steep while you pull the rest of the ingredients together, about 10 minutes.
Put the shrimp in a bowl of cold water with 1 tablespoon salt and set aside.
Heat a large non-reactive skillet over medium heat. Add one tablespoon of the butter and oil and when the butter melts, add the cumin seeds, mustard seeds and turmeric and cook until the seeds pop, about 2 minutes. Add the chiles and ginger and cook, stirring until lightly toasted, scraping the pan with a wooden spoon so the ginger toasts but doesn't stick, about 3 minutes.
Add the corn, strain the corn-and-milk broth to the pan and bring to a low simmer over medium heat. Discard the cobs. Season with 3/4 teaspoon salt and some pepper. Cook until the liquid reduces to coat the corn in a light sauce, 5 to 7 minutes. (The corn can be prepared ahead to this point.)
Drain the shrimp well. Turn the heat down to medium-low and add the shrimp with the curry leaves, if using, and cook in the corn, covered, stirring periodically, until they curl and turn light pink, about 4 minutes. (If using cilantro, add after the shrimp are cooked). Whisk in the remaining tablespoon butter. Serve with lime wedges and tomato chutney.