Preheat oven to 350°F. Grease an 8x6" pyrex dish and set aside.
In a large mixing bowl, combine sugar, applesauce, coconut milk, and vanilla.
Use a sieve to sift in the flour and baking powder, then whisk until smooth.
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.
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.