Preheat the oven to 350 degrees. Grease 9x13 inch baking dish.
In a medium bowl, whisk together the eggs, vanilla and milk. In a separate larger bowl, stir together the rice flour, sugar, and baking powder. Pour the wet ingredients into the dry ingredients and stir to blend. Mix in melted butter. Pour into the prepared pan.
Bake for 1 hour in the preheated oven. Cool completely, then cut into squares to serve.