Preheat the oven to 350ºF and adjust the rack to the middle position. Using a pastry brush, butter or oil a 13×18-inch cookie sheet and then line it with parchment paper. Place the eggs and sugar in the bowl of a standing mixer with the beater attached. Mix on medium-high for 8 minutes until thick and pale yellow. Fold in the pumpkin.
Place the coconut flour, tapioca, arrowroot, baking powder, baking soda, pumpkin pie spice, and sea salt in a medium bowl. Whisk to combine and remove any clumps. Fold the flour mixture into the egg mixture.
Pour the cake batter onto the prepared cookie sheet and gently spread the cake batter with a spatula so it’s even across the pan. Bake for 12 minutes. Remove from the oven and let sit for 5 minutes. Sprinkle the cake with a small amount of arrowroot and then place a large dishtowel that covers the entire cake over the cake. Grasp both ends of the pan and dishcloth (make sure to wear oven mitts) and quickly turn the cake upside down onto the dishcloth. Carefully peel off the parchment paper. Roll up the cake and the towel together, starting at one of the narrow edges. Cool completely.
Place the ½ cup maple sugar and 2 teaspoons arrowroot flour in a coffee grinder and grind until it’s a fine powder. Place the cream cheese, sugar mixture, butter and vanilla extract in a bowl and beat with a mixer until fluffy, about 2 minutes.
Carefully unroll the cake. Using a spatula, spread the cream cheese over the cake and then reroll the cake. Serve immediately, or cover and refrigerate until ready to serve.