Preheat oven to 350°F. Grease an 8x8" baking dish and set aside.
Combine sweet potato puree, sugar, coconut milk, and vanilla in a large bowl.
Use a sieve to sift in the flour and baking powder, then whisk until smooth.
Scoop out about ¼ cup of batter and mix with ground black sesame seeds and ¼ cup plant-based milk.
Mochiko has a tendency to clump together, so if your batter has lumps of flour in it, arrange a sieve over your baking dish or a bowl. Pour some batter in the sieve and use a spatula to press the batter down, smoothing out any clumps. Repeat with remaining batter. OR if your batter is fairly smooth, just transfer to the prepared baking dish.
Dollop the black sesame mixture on top of the batter and use a toothpick or knife to make swirls in the batter.
Tap the dish on the countertop a few times to release air bubbles from the batter. Bake for 45-60 minutes, until the top begins to crack and the edges are slightly brown.
Let the mochi cake cool completely to room temperature before slicing. Store leftovers in an airtight container at room temperature for up to 3 days.
SWEET POTATO: I recommend Japanese sweet potatoes (satsumaimo) if you can find them, but any variety should work.