Preheat the oven to 350°F (175°C). Line a 12-cup muffin tin with paper liners or grease with non-stick cooking spray.
In a medium bowl, whisk together the all-purpose flour, baking powder, salt, and ground cinnamon. Set aside.
In a large bowl, cream the softened butter and granulated sugar together until light and fluffy. Beat in the eggs one at a time, then stir in the vanilla extract and applesauce until well blended.
Gradually fold the dry ingredients into the wet ingredients, mixing gently just until combined. Be careful not to overmix the batter.
Divide the batter evenly among the prepared muffin cups, filling each about two-thirds full.
Bake for 15 to 18 minutes, or until the tops are golden brown and a toothpick inserted into the center of a muffin comes out clean.
Allow the muffins to cool in the tin for 5 minutes before transferring them to a wire rack to cool completely.
Notes
Store in an airtight container at room temperature for up to 3 days, or freeze for up to 3 months.