Preheat the oven to 350°. Grease and flour a 9x13-inch baking pan.
Using an electric mixer (hand mixer or stand mixer is fine) beat the butter and sugar until light and fluffy.
Add the eggs and beat until fully mixed with the butter and sugar.
Add water to the can of coconut milk to equal 2 cups. (I pour the can of coconut milk into a 2 cup measuring cup and then add water to the 2 cup line.)
Add 4 ounces of water to the 12 oz can of evaporated milk to make a total of 2 cups.
Put all of the milk and water mixture, mochiko flour, baking powder, and vanilla into the creamed egg mixture. Mix well.
Pour the batter into the greased 9x13-inch baking pan. Sprinkle toasted sesame seeds on top (if desired). Bake at 350° for 1 hour.
Cool completely before cutting the mochi into squares for serving.