Preheat the oven to 350ºF and adjust the rack to the middle position. Thoroughly butter a mini Bundt cake pan.
Place the eggs and maple sugar in the bowl of a standing mixer with a whisk attachment. Whisk on medium-high for 8 minutes, then slowly whisk in the cooled coconut oil and pumpkin. Sift the coconut flour, arrowroot flour and pumpkin spice blend over the egg mixture and gently fold in until incorporated. Stir in the vanilla. Let the batter sit for 10 minutes at room temperature.
Spoon the batter into the buttered pan. Bake for 23-25 minutes, or until just turning golden brown on the edges. Let the cakes cool for 10 minutes and then invert them onto a cooling rack. Serve warm or at room temperature.