Preheat oven to 400 degrees F (200 degrees C). Lightly grease muffin tins.
Stir together the cornbread mix and the brown sugar in a large bowl. Whisk the eggs and milk in a small bowl until smooth. Fold the eggs and cheese into the dry mixture until moistened. Add the hot dogs to the batter. Spoon mixture into greased muffin tins until 2/3 full. (I used baking non-stick spray with no liners, as I found cupcake liners stuck to the cornbread after it baked.)
Bake in a preheated oven 14 to 18 minutes, or until golden brown.