In a large bowl or the bowl of your stand mixer, stir oil, sugars and apple butter together until smooth. Beat in eggs and vanilla until completely combined. In a separate bowl, combine flour, baking powder, baking soda, cinnamon, nutmeg and salt. In another bowl, combine apple cider and milk. Alternate adding the dry and wet ingredients to the batter until everything is just combined. Don't overmix! Fold in chopped apples. Scoop batter into prepared muffin tin about 3/4 high. Bake for 13-16 minutes or until a toothpick inserted in the center of muffins comes out clean.