Preheat your oven to 350°F. Grease or line a mini muffin tin (or regular muffin tin) with paper liners.
In a large bowl, stir in the pumpkin puree, eggs, applesauce, vanilla extract, and milk. Whisk everything together until well combined.
In a separate bowl, combine the flour, baking soda, baking powder, cinnamon, nutmeg, and salt. Stir until well mixed.
Slowly add the dry ingredients into the wet ingredients and stir just until combined. Avoid over-mixing, as this can make the muffins dense.
Spoon the batter into the prepared muffin tin, filling each cup about 2/3 full. You can use a mini muffin tin for smaller, toddler-sized portions or a regular tin for larger muffins.
Bake for 15-18 minutes for mini muffins (or 20-22 minutes for regular-sized muffins), or until a toothpick inserted into the center comes out clean.