In a small bowl, combine the flour, baking powder, baking soda, pumpkin spice, cinnamon, and sea salt. Mix well and set aside.
In a large mixing bowl, cream together the vegan butter and sugar using a stand mixer or hand mixer for about 5 minutes until well combined.
Stir in the vanilla extract and pumpkin purée, blending for another 3 minutes and scraping down the bowl to ensure everything is mixed properly.
Gradually add the dry ingredients to the wet mixture in two parts, mixing until just combined. Scrape the sides and gently fold to incorporate any remaining dough.
Shape the dough into a large ball or two smaller ones, cover with plastic wrap, and refrigerate for at least 2 hours to firm up.
Preheat your oven to 350°F.
Once chilled, remove the wrap and scoop out 1-2 tablespoons of dough, rolling them into balls. Place them on a lined cookie sheet, ensuring there's enough space between each ball. Keep them higher rather than wider to maintain thickness.
Chill the dough balls in the fridge for another 10 minutes. Bake for 10-13 minutes for smaller cookies or 12-15 minutes for larger ones; the larger ones will be soft but slightly firmer after 15 minutes.
After baking, let the cookies cool for exactly 10 minutes. Top with cream cheese frosting and sprinkle with pumpkin spice before serving.