Combine the cheese, cream cheese, butter and chipotles in a large bowl and beat with an electric mixer until smooth. Scoop the cheese mixture into 4 balls on a baking sheet using a medium ice cream scoop. Freeze until hard, about 1 hour.
Preheat the oven to 400 degrees F. Spray 4 tall 8-ounce ramekins (ours were 2 inches tall on the outside and 3 1/2 inches wide) with nonstick cooking spray and dust lightly with flour.
Whisk together the flour, cornmeal, sugar, baking powder and salt in a large bowl. Whisk together the milk, oil and egg in a small bowl. Whisk the wet ingredients into the dry until smooth.
Put 2 tablespoons of the batter into each prepared ramekin to coat the bottom. Put one cheese scoop in the middle of the batter in each ramekin, making sure there is a 1/4-inch border all the way around the cheese mixture (you do not want it to touch the sides). Divide the remaining batter among the ramekins and place on a baking sheet. Bake until puffed and slightly golden around the edges, about 25 minutes. Let cool 5 minutes. Invert onto a plate, top with a pat of butter and serve.
When measuring flour, we spoon it into a dry measuring cup and level off excess. (Scooping directly from the bag compacts the flour, resulting in dry baked goods.)
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