Preheat the oven to 350°F. Lightly grease the short sides of a 10x4½-inch loaf pan with ghee or coconut oil. Line the bottom and long sides of the pan with parchment paper so the ends hang over the sides.

In a stand mixer fitted with the beater attachment, or using an electric handheld mixer, beat the eggs, honey, coconut sugar, palm shortening, and vanilla on medium speed for 30 seconds. Scrape down the sides of the bowl, then add the coconut flour, arrowroot, baking powder, baking soda, and salt. Beat on high for 30 seconds, until smooth. Add the mashed banana and beat on medium-low speed until just incorporated.

Pour the batter into the prepared loaf pan and gently smooth the top with a spatula. Bake for 50-55 minutes, until a toothpick inserted into the center of the loaf comes out clean. Cool in the pan for 20 minutes, then gently lift the parchment to remove the loaf from the pan. Cool completely on a wire rack, about 4 hours.

To store, once the loaf is fully cooled, wrap it in a piece of parchment paper and seal it in a resealable plastic bag or wrap it tightly in plastic wrap. It will keep in the refrigerator for 10 days. To serve, cut the loaf into ¼-inch thick slices.

Freeze slices of bread in a single layer on a rimmed baking sheet, tightly covered with plastic wrap, for 4 hours. Transfer the frozen slices to an airtight container and store in the freezer for 3 months. Defrost in the refrigerator overnight or defrost from frozen in a 300°F oven for 10 minutes.