Preheat oven to 400ºF (200ºC).
In a large mixing bowl, whisk together eggs, butter and sugar until smooth. Fold in pumpkin and vanilla and continue mixing until well combined. Add flour, baking powder, baking soda, salt and spices and mix together until all the dry ingredients have been fully absorbed.
Using a piping bag, transfer batter to doughnut pans to form 12 equally sized pieces, smoothing out the tops with a rubber spatula if needed. Bake for 10-12 minutes until golden and they spring back to the touch.
Once the doughnuts have finished baking, transfer pans to a wire cooling rack and let sit until doughnuts have cooled (about 30 minutes).
To make the glaze, add cream cheese, maple syrup, milk and salt to a small bowl and whisk together until smooth.
Transfer doughnuts to a large baking sheet. Drizzle with glaze, sprinkle with chopped pecans and serve.