Bake the sweet potato on a baking sheet in a preheated 375°F oven for 1 hour, until easily pierced with a knife. Remove from the oven, cool, and peel. Purée in a food processor; you should end up with roughly 1 1/2 cups., Generously butter a 2-quart baking dish with straight sides. Place a rack in the center of the oven and preheat to 375°F., In a medium saucepan, heat the milk, sugar, salt, and cayenne until bubbles form around the edges. Whisk in the cornmeal and cook for about 2 minutes, stirring constantly, until the mixture thickens and a thin film coats the bottom of the pan. Remove the thickened mixture from the heat, and stir in the butter a tablespoon at a time., In a large bowl, whisk together the egg yolks and heavy cream until the yolks are fully incorporated and the cream is a uniform pale yellow., In the bowl of your mixer fitted with the whisk attachment, whip the egg whites until they form soft peaks., Once the cornmeal mixture has cooled for at least 5 minutes, whisk 1/3 of it into the egg yolks and cream. Follow up with the remaining cornmeal mixture to create a pour-able batter. Using a spatula, stir in the grated cheese, sweet potato purée, and poblano peppers. Finally, fold in half of the whipped egg whites. Continue with the remaining whites., Pour the batter into the prepared baking dish and bake for 35 to 40 minutes., Store any leftovers covered in the refrigerator for up to 5 days.