Preheat your oven to 350°F (175°C).
In a bowl, whisk together flour, sugar, baking powder, cinnamon, and salt.
In another bowl, mix together pumpkin puree, eggs, vegetable oil, and vanilla extract until well blended.
Gradually fold the dry ingredients into the wet mixture until just combined.
Using a piping bag or a spoon, fill each donut cavity about ¾ full.
Place the donut pan in the preheated oven and bake for 15-18 minutes.
Allow the donuts to cool in the pan for about 5 minutes before transferring them to a wire rack.
For an optional glaze, mix powdered sugar with a bit of milk and vanilla to drizzle on cooled donuts.