Prep. Preheat oven to 350°F (175°C). Line a muffin tin with paper liners.
Wet Ingredients + Sugar. In a large bowl, whisk together the sourdough discard, oil, sugars, and eggs until smooth and well blended.
Add Dry Ingredients. Add the flour, baking powder, salt, and cinnamon. (There's really no need for a separate bowl, put it right on top. Mix a bit by hand, add the mix, and keep mixing just until everything is combined.
Add Apples. Gently fold in the diced apples.
Bake. Divide the batter evenly among the muffin cups. Bake for 22-27 minutes, or until a toothpick inserted into the center comes out clean. (Sourdough discard may require a slightly longer bake time.)
Cool. Let muffins cool in the pan for a few minutes, then transfer to a wire rack to cool completely.
Make the Glaze. While muffins cool, whisk together the glaze ingredients in a small bowl. If too thick, add milk 1 tablespoon at a time until the desired consistency is reached.
Drizzle Glaze on Top. Drizzle the glaze over the cooled muffins and allow to set before serving.