Preheat the oven to 350 degrees F.
Spray bundt pan with non-stick cooking spray or grease with oil and then dust well with flour.
In a large bowl, whisk together the eggs, oil, applesauce, sugar and vanilla until well combined.
Add pumpkin and whisk well to combine.
Add the baking soda, pumpkin pie spice, and salt, and mix to combine.
Add the flour and mix with a rubber spatula until just combined. Do not over-mix.
Pour into the prepared bundt pan.
Bake for 55-65 minutes, checking after 55 minutes with a toothpick to ensure doneness and adding more time as needed.
Cool the cake in the bundt pan for 10-15 minutes.
Carefully invert onto a wire rack until completely cooled.