In a small pot over medium heat, add in your milk and butter. Do not let the milk boil but heat the mixture enough until the butter melts.
In a bowl, beat together the egg, sugar and vanilla. Then slowly, drizzle the milk/butter mixture into the egg mixture while whisking vigorously.
Add the glutinous flour, tapioca flour, milk powder and salt into the egg mixture and whisk until well combined. Pass the mixture through a sieve to remove any lumps. Place the mixture inside the fridge.
Pre-heat your oven to 180C/350F. Grease your pan with softened butter generously. Once the oven is pre-heated, pour the mixture into your greased pan 90% full. Bake for 35-40 minutes.
Once baked, flip the butter mochi out of the pan and allow it to cool on a wire rack upside down to prevent sinking.