Heat oven to 400ºF. Grease a 12-cup muffin tin.
In a large bowl, stir together the cornmeal, flour, sugar, baking powder, and salt, until combined. In a second bowl, whisk together the egg and melted butter. Put the wet ingredients into the dry ingredients and stir until just combined. Let the batter sit 5-10 minutes.
Fold in the corn kernels, grated apple, and shredded cheddar.
Divide the batter among the 12 prepared muffin cups. Bake 18-22 minutes, or until the edges of the muffins begin to pull away from the edges of the pan and a toothpick inserted into a muffin comes out clean.
Remove from the oven and let cool. Meanwhile, add the softened butter and honey to a bowl. Mix until smooth; season to taste with salt.
Serve the muffins with honey butter. (Extra butter can be kept in the refrigerator.)