1. Carefully remove the husks and silk from the ears of corn; make a cut slightly above the base of the corn, if necessary, to release the inner husks. Arrange the husks in 2 piles, the thick outer layers and the paler green, thinner ones. Cut the kernels from the cobs, stopping when you have 2 cups.
2. Heat the olive oil in a large saucepan. Add the mushrooms; season with salt and pepper. Cover and cook over moderate heat, stirring occasionally, until they begin to brown, about 8 minutes. Uncover, add the garlic and cook, stirring, until the garlic is fragrant and the mushrooms are browned, about 4 minutes. Season with salt and pepper and stir in the parsley. Transfer to a plate.
3. Add the water to the saucepan and bring to a boil. Add the corn and 1 teaspoon of salt. Cover and cook over moderate heat until tender, 4 minutes. Slowly whisk in the polenta over low heat until thickened, about 4 minutes. Remove from the heat. Stir in the Parmesan and butter. Season with salt and pepper.
4. To assemble the tamales, spread 2 outer husks on a work surface, overlapping them at their base ends by 3 inches. If necessary, lay 2 large knives along opposite edges of the husks to keep them open. Spread 1/3 cup of the polenta in the center of the husks to within 1/2 inch of the edge to form a 4-by-2-inch rectangle 1 inch thick. Press 2 sticks of cheese into the polenta and top each tamale with one-sixth of the mushrooms and garlic. Cover the mushrooms with 2 large inner husks, overlapping them at their base ends. Tie the ends with kitchen string. Repeat with the remaining husks and ingredients.
5. Light a grill. Lightly brush the grate with vegetable oil and grill the tamales, outer husk side down, over a medium-hot fire for about 4 minutes, or until nicely browned. Carefully flip the tamales and grill for 2 minutes longer. Invert onto plates and serve at once with hot sauce or tomato salsa.
Make Ahead: The uncooked tamales can be refrigerated overnight.
Wine Recommendation: The sweet summer corn and creamy polenta will find an ideal partner in a big, buttery Chardonnay with some sweet, smoky oak. Choose a flavorful example from California, such as the 1999 Meridian Santa Barbara.