Preheat oven to 400°F (200°C).

In a bowl, blend milk and prepared mustard.

Add the beaten egg to the milk mixture and stir to combine.

In a separate bowl, combine the corn muffin mix and Parmesan cheese.

Add the wet milk mixture to the dry corn muffin mixture.

Stir until just mixed; do not overmix.

Pour the batter into an 8 x 8 x 2-inch baking pan.

Bake in the preheated oven for 18 to 20 minutes.

Sprinkle the shredded Cheddar cheese evenly over the top of the corn bread.

Bake for 1 minute longer, or until the cheese is slightly melted.

Serve warm.