Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.
In a large mixing bowl, whisk together the softened butter, brown sugar, and granulated sugar until the mixture is smooth and creamy, with a slight gloss.
Add the egg and vanilla extract to the creamed mixture and whisk until fully incorporated, resulting in a fluffy, homogeneous base.
Mix in the pumpkin puree until the batter is smooth and evenly colored, giving a vibrant orange hue that hints at fall flavors.
In a separate bowl, combine the sifted flour, cinnamon, cardamom, baking powder, and salt. Whisk to evenly distribute the spices and leavening agents.
Gradually fold the dry ingredients into the wet mixture using a spatula, mixing just until combined and the dough comes together softly.
Using a cookie scoop or spoon, portion out the dough onto the prepared baking sheet, spacing each cookie about 2 inches apart to allow for spreading.
Bake in the oven for about 12 minutes, or until the edges are lightly golden and the centers look set but still soft.
Remove the baking sheet from the oven and let the cookies cool on the sheet for 5 minutes to firm up before transferring them to a cooling rack.
Place the cookies on a wire rack and allow them to cool completely, revealing their cracked, rustic surface and tender texture.
Once cooled, serve your pumpkin-spiced cookies alongside a warm beverage for a cozy treat.