Preheat oven to 325°. Arrange over rack in the middle of the oven.
In the work bowl of a stand mixer, cream butter and sugar together until fluffy, about 3 minutes. Add eggs one at a time and mix until just incorporated after each addition.
In a mixing bowl, combine corn meal, salt and baking powder. With the mixer on low, slowly add the dry ingredients into the wet ingredients until just combined. Fold in poblano chile, corn and cheddar cheese with a wooden spoon.
Transfer batter to a 10-inch cast iron skillet and bake until golden and just cooked through, about 15 to 18 minutes. Serve immediately.
Recipe courtesy of Chef Jose Garces.