Place the cubed taro in a pot filled with boiling water.
Cook the taro for 15-20 minutes, until fork-tender.
Drain the taro and while hot, mash the mixture with a fork (or potato masher).
While the taro is still hot, add in the coconut oil, condensed milk/sugar and mix until combined. (If you prefer a purple hue, you can add in purple sweet potato powder).
Note: if you prefer a silky smooth texture, you can run it through a food processor.
Let cool and store in an airtight container in the fridge until ready to use.
Bake the Swiss Roll Cake:
Line a 9"x13" tray with parchment.
Separate egg whites and yolks.
Whisk yolks with sugar, oil, milk, vanilla, then sift in flour.
Beat egg whites with cream of tartar, gradually adding sugar, until soft peaks form.
Gently fold whites into yolk mixture in thirds.
Pour batter into tray, tap to release air bubbles, and bake at 375°F/191°C for 14–15 minutes until golden and springy.
Drop the cake pan from a small height to prevent shrinkage, then cool on a rack until slightly warm.
Assemble the roll:
Once the cake is slightly warm (not hot), spread a thin, even layer of taro paste over the cake.
Carefully roll the cake, using parchment to guide.
Wrap tightly in parchment or plastic wrap.
Chill in the fridge for 1-2 hours to set.
When ready to serve, use a sharp serrated knife to cut into slices.