1) Preheat oven to 400 degrees F. Butter a muffin tin.
2) In a large bowl, whisk together flour, cornmeal, sugar, baking powder, baking soda, salt, and chili powder. In a separate bowl mix together buttermilk, butter, eggs, and thawed, mashed sweet corn.
3) Stir wet ingredients into the dry stuff. Batter should be very thick.
4) Spoon half the batter into the buttered muffin tins. Add a big chunk of cheddar cheese right in the middle of each muffin. Then cover with more batter.
5) Bake muffins for 20 minutes at 400 degrees F. in the middle of the oven. Rotate once halfway through baking.
Remove and let cool for a minute before removing muffins, but serve while warm so cheese is melted.