Step 1: Preheat your oven to 350°F (175°C). Line a standard 12-cup muffin tin with paper liners or grease it lightly.
Step 2: In a medium bowl, whisk together the dry ingredients: flour, baking soda, baking powder, cinnamon, nutmeg, and salt. Set this aside.
Step 3: In a large mixing bowl, combine the granulated sugar, brown sugar, and vegetable oil. Whisk until thoroughly combined and smooth.
Step 4: Add the unsweetened applesauce, eggs, and vanilla extract to the sugar-oil mixture. Stir until all the wet ingredients are well incorporated.
Step 5: Gradually add the dry ingredient mixture to the wet ingredients. Stir gently with a spoon or spatula until just combined. Be careful not to overmix; a few lumps are perfectly normal and help keep the muffins tender.
Step 6: If desired, fold in any optional additions like chopped nuts, raisins, or chocolate chips at this stage.
Step 7: Divide the batter evenly among the prepared muffin cups, filling each about two-thirds full.
Step 8: Bake in the preheated oven for 18-20 minutes, or until a wooden toothpick inserted into the center of a muffin comes out clean.
Step 9: Remove the muffins from the oven and let them cool in the muffin tin for about 5 minutes. Then, transfer them to a wire rack to cool completely.