Preheat the oven to 350°F (175°C).
In a large bowl, whisk together the dry ingredients: flour, baking soda, cinnamon, nutmeg, and salt.
In another bowl, whisk together the wet ingredients: eggs, melted butter, honey, applesauce, milk, and vanilla extract.
Sift the dry ingredients into the wet mixture and stir until just combined. Do not overmix.
Fold in the grated apple and diced apple.
Divide the batter evenly among muffin cups.
Bake for 15–20 minutes, or until a toothpick inserted into the center comes out clean.
Let the muffins cool in the pan for 5 minutes, then transfer them to a wire rack to cool completely.
To make the cream cheese frosting, mix softened cream cheese, powdered sugar, and milk until smooth.
Drizzle the cooled muffins with the cream cheese frosting.