Preheat oven to 375 degrees and line standard-size muffin tins with paper liners. Spray the liners with nonstick spray.
In a large mixing bowl, whisk flour, baking soda, salt, cinnamon, brown sugar, and granulated sugar together. Set aside.
In another mixing bowl, whisk eggs, oil, vanilla, applesauce, and sour cream until smooth.
Add the flour mixture to the egg mixture and mix gently until just combined. Do not overmix.
Scoop the muffin batter into each muffin liner, filling ¾ (or a bit more) full.
Bake at 375 degrees for 17-20 minutes, or until a toothpick inserted into the center of the muffin comes out clean. Cool for a few minutes in the muffin tin, and then remove the muffins to cool on a cooling rack.
Once cooled, keep the muffins at room temperature in an airtight container. These will freeze well for up to three months.