Preheat oven to 200 C / 400 F.
Line a regular muffin tin with paper liners.
In a large bowl, whisk together the flours, cornmeal, sugar, salt, dry mustard, and baking powder.
In a medium bowl, whisk together the melted butter, milk, and eggs.
Stir the wet ingredients into the dry. Mix just until blended.
Gently mix in the ham and 3/4 cup grated cheese.
Divide the batter into the muffin tin. Fill each muffin until full.
Sprinkle over the reserved 1/4 cup cheese over the muffins.
Bake for 20-25 minutes or until a wooden skewer inserted to the centre of a muffin comes out clean.
Remove from oven and let cool.