Preheat the oven to 350°F (175°C). Line a muffin tin with paper liners or grease with cooking spray.
In a large bowl, whisk together the flour, granulated sugar, baking powder, baking soda, cinnamon, nutmeg, and salt.
In another bowl, mix the pumpkin puree, applesauce, vegetable oil, eggs, and vanilla extract until well combined.
Pour the wet ingredients into the dry ingredients and stir until just combined. Do not overmix; a few lumps are okay.
In a separate small bowl, combine the rolled oats, brown sugar, flour, and cinnamon for the streusel topping. Stir in the melted butter until the mixture resembles coarse crumbs.
Scoop the muffin batter into the prepared muffin tin, filling each cup about two-thirds full. Sprinkle the streusel topping evenly over each muffin.
Bake for 18-20 minutes or until a toothpick inserted into the center comes out clean. Allow the muffins to cool in the pan for 5 minutes before transferring them to a wire rack to cool completely.