Whisk together dry ingredients in a large bowl. In a medium bowl, beat eggs until frothy and stir in milk. Add small amounts of milk mixture to the melted butter if it needs cooling down, then pour butter into milk mixture.
Pour into the dry ingredients and stir until flours are fully incorporated. Add in the cheese. The batter should be thick.
Fill muffin cups 2/3 to 3/4 full. Muffins should rise while baking and not spill out.