Preheat oven to 350 degrees.
Combine flours, baking soda, baking powder, and salt in a bowl, and stir to combine.
In a separate bowl whisk the eggs, oil and maple syrup and stir to combine. Add the buttermilk to the egg mixture and stir.
Add the buttermilk mixture to the flour and stir until just combined. Fold in the cheese and ham.
Scoop the batter 2/3 of the way up into greased muffin cups and bake for 18-20 minutes (15 minutes if using mini muffin cups).