Cut the tops off the bell peppers and remove the seeds and ribs. Slice each chile in 1/2 from stem end to blossom end. Arrange in a shallow, buttered baking dish.
Melt the butter in a saucepan over medium heat. Add the onion and garlic and cook until the onion softens, 3 to 4 minutes. Add the cornmeal and stir to mix. Slowly pour in the chicken broth, stirring to combine. Add the cream, corn, basil, cilantro, salt, and 1/4 cup of the Parmesan. Cook, stirring constantly with a wooden spoon, until the polenta becomes as thick, about 10 minutes. Remove from heat.
Meanwhile, preheat the oven to 375 degrees F.
Fill the bell peppers with the polenta. Sprinkle with the remaining Parmesan and the Gruyere. Bake for 20 to 25 minutes, until golden and bubbling. Serve hot. (The peppers can be stuffed and baked the preceding day. To serve, bring to room temperature and reheat at 350 degrees F, for about 12 minutes).
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