Heat the oven to 350°F with a rack in the middle position. Coat a 13-by-9-inch metal baking pan with coconut oil. Place the sweet potatoes in a microwave-safe medium bowl, cover and microwave on high for about 5 minutes, stirring once halfway though, until the potatoes are completely tender. Carefully uncover and set aside to cool slightly.

In a food processor, combine the flour, coconut, ginger, baking powder, baking soda and salt. Process until the coconut is finely ground, 1 to 2 minutes.

Transfer to a large bowl. In the processor, combine the brown sugar and lime zest, then process until fragrant, about 30 seconds. Add the sweet potatoes and process until completely smooth, 60 to 90 seconds, scraping the bowl as needed.

Add the eggs, milk and vanilla, then process until combined, about 10 seconds. With the machine running, add the melted coconut oil through the feed tube, then process until fully incorporated.

Pour the sweet potato mixture into the dry ingredients and gently whisk to combine. Transfer the batter to the prepared pan and spread evenly.

Bake until the cake is golden brown and a toothpick inserted at the center comes out clean, 30 to 35 minutes. Let cool in the pan on a wire rack for 15 minutes.

Meanwhile, in a small bowl, whisk the powdered sugar and the lime juice until smooth. Brush the glaze evenly onto the warm cake. Let the cake cool completely, about 2 hours.