In a medium mixing bowl, whisk together the dairy-free milk and apple cider vinegar. Set aside for 5 to 10 minutes. This is your vegan "buttermilk."
In a separate large bowl or bowl of a stand mixer, combine the brown rice flour, coconut sugar, oat flour, tapioca flour, pumpkin pie spice, baking powder, baking soda, and sea salt. Stir to blend.
To the bowl with the buttermilk, whisk in the eggs, pumpkin puree, maple syrup, and vanilla extract until creamy.
Transfer the wet ingredients to the bowl with the flour mixture. Beat until a batter is formed. Allow the batter to rest in the bowl at room temperature for 30 minutes.
Meanwhile, preheat the oven to 350 degrees F. Spray the bottom of an 8x8 baking pan with cooking spray and line with parchment paper, allowing a 2-inch overhang on one of the sides.
Pour the batter into the baking pan and bake for 45 to 55 minutes, or until a toothpick inserted comes out clean and if you are using a digital thermometer, the internal temperature reaches 195 to 200 degrees F. Allow the bread to cool in the baking pan (at least one hour) before removing and slicing into squares.