In a medium bowl lightly whisk eggs. Add applesauce and stir together.
Add vanilla extract and sugar to egg mixture, stir to dissolve sugars.
In a large bowl mix together flour, baking powder, salt, cinnamon.
Combine the wet ingredients and carrots with the dry ingredients. Stir with a wooden spoon until just combined, about 25 strokes.
Heat oven to 350 degrees.
Scoop batter with a muffin scoop into paper cups. Bake until muffins are lightly golden, about 18-20 minutes. Insert a toothpick in center, if it comes out clean they are done.
Recipe by Pick Fresh Foods at https://pickfreshfoods.com/carrot-cake-muffins/