Preheat oven to 350 degrees F. Heat a small skillet over medium-low heat and add diced apples with 3 tablespoons apple cider, and a pinch of cinnamon and salt. Cook, stirring occasionally, until apples are soft and caramely, about 8-10 minutes. In a bowl, whisk together flour, oats, baking soda, baking powder, salt and spices. Set aside. Line a muffin tin with liners.
In a large bowl, whisk egg and brown sugar together until smooth and no lumps remain. Add in vanilla extract, butter, apple sauce and apple cider, whisking again until smooth. Gradually add in dry ingredients, mixing until just combined. Fold in diced apples. Do not overmix! Fill each muffin liner 2/3 of the way full with batter (I use an ice cream scoop to get the muffins to be of equal size).
Bake for 15-17 minutes, or until tops are no longer wet and become slightly golden. Top with glaze if desired!