Heat the oven to 350°F. Lightly butter a 9” x 13” inch cake pan, then line the bottom and sides with parchment paper.
In a large bowl, whisk the eggs and sugar until the sugar dissolves. Whisk in the coconut milk, evaporated milk, butter and vanilla. Continue whisking while gradually adding the mochiko, baking powder, and salt. Whisk until the batter is completely smooth. Pour into the prepared pan, then tap it against the counter to get rid of any air bubbles.
Bake until golden brown and the center bounces back when pressed, 1 to 1½ hours. Cool completely in the pan set on a wire rack. Use the parchment paper to slide out of the pan.
Cut into squares and serve.