Cut the softened vegan butter into 1" cubes and add them to a large bowl. Add the caster sugar, soft brown sugar, pumpkin puree, aquafaba, and vanilla extract to the bowl with the butter. Use a handheld electric whisk or stand mixer to beat the ingredients until creamed together. You can use a regular whisk as well, it will just take a little longer to mix the ingredients!
In a separate bowl, combine the flour, baking soda, salt, and pumpkin spice. Stir the dry ingredients so that they are mixed evenly.
Add the dry ingredients to the wet ingredients and fold them together using a spatula until they form a dough consistency.
Chop the chocolate into small chunks and them to the cookie dough. Fold them through the dough as evenly as possible. Cover the bowl with the cookie dough with some clingfilm or a plate and chill in the fridge for 20 minutes.
Preheat your oven to 180°C (356°F) while the cookie dough is chilling. Line 2 large baking trays with some parchment paper.
Roll the cookie dough into golf ball-sized balls. Be careful to leave at least 2.5" of space between each ball of dough as they will spread whilst baking!
Bake the cookies for 11-12 minutes. After the first 5 minutes of baking, take them out of the oven and tap the tray on your work surface to help the cookies spread and crinkle on top.
Bake for the remaining 6-7 minutes and remove from the oven. Bang the trays on your work surface again and then let the cookies sit on the baking trays for 2-3 minutes. Next, carefully slide the sheet of parchment paper with the cookies off of the tray and onto a cooling rack. Once they have cooled for 10-15 minutes, also remove the parchment paper and allow them to continue to rest until cool.
Garnish with Maldon flakes or sea salt.
Store in an airtight container at room temperature and consume within 5 days.