Preheat oven to 350°F (177°C). Prepare a baking sheet with parchment paper, or silicon baking mat, etc.
Whisk the flour, baking powder, baking soda, salt, nutmeg, cinnamon, and ginger together in a large bowl. Stir in half the chopped walnuts (1/2 cup). Set aside.
In a large bowl, whisk together both sugars, pumpkin puree, egg white, molasses, and vanilla until smooth. The mixture should be well combined.
Add the dry ingredients to the wet ingredients and stir until just combined. Dough will be thick and sticky.
Scoop cookie dough, around 1.5 tablespoons per cookie, and place 3 inches apart on baking sheets. Gently press the remaining chopped walnuts (1/2 cup) onto the top of each cookie.
Bake for 13-15 minutes or until edges appear set. Centers will look soft. Remove from oven and allow cookies to cool on the baking sheet for 10 minutes before transferring to a wire rack. These cookies improve in flavor after cooling—they're even better the next day.