Preheat your oven to 175°C (350°F). Line an 8" loaf tin with parchment paper and set it aside.
To make the vegan "buttermilk" add the soy milk and apple cider vinegar to a small bowl, stir and allow to sit for 10 minutes. Prepare the flax egg by mixing the milled flaxseed with 2 tablespoons of water, allow to sit and soak for at least 5 minutes.
In a large bowl, mix together the vegan buttermilk, flax egg, pumpkin puree, maple syrup, olive oil, and vanilla. Set aside.
In a separate bowl, combine the flour, ground pecans, light brown sugar, baking powder, pumpkin spice, and salt, and stir to evenly combine the ingredients. Add the flour mixture to the large bowl with the wet ingredients and use a spatula to carefully fold the ingredients together.
Add the cake batter to the prepared loaf pan and bake for 50-60 mins. Check the cake is ready by inserting a skewer or toothpick into it, which should come out clean. If there is cake residue on your toothpick or skewer, return it to the oven to continue baking for another 5-10 minutes. Allow the cake to cool in the pan for about 10 minutes before transferring it to a cooling rack.