Preheat oven to 170°C and butter and line 2 x 21cm cake tins with paper.
Place butter into a stand mixer and beat until butter is softened.
Add yoghurt, milk, vanilla and eggs and mix until light and airy and well combined.
Add sugar, flour and baking powder, bicarb soda and salt. Mix until the batter comes together, finishing by hand if needed.
Divide batter between tins and tap gently to level tops of cake.
Bake for 40-45 minutes until golden and springing back to the touch. Cool for 15 minutes in the tin before removing from tins.
Cool completely before finishing cakes as directed.
Make a roux with the flour and milk by stirring briskly together over a medium heat until thickened. Pour into bowl, cover with plastic wrap, pushing plastic down onto surface of mixture. Cool completely.
Aerate the butter by whipping it with either a hand held beater or in a stand mixer, until it is softened and creamy. Add the sugar and vanilla bean paste and whip again until combined.
Add cooked and cooled roux mixture and continue to beat for around 2 minutes until very smooth and white. Cover and refrigerate for 15 minutes. Use immediately.