Preheat oven to 350°F (175°C). Grease and line two 8-inch round cake pans.
In a medium bowl, whisk together flour, baking powder, baking soda, and salt.
In a large bowl, cream butter and sugar until pale and fluffy. Beat in eggs one at a time, then add vanilla.
Alternate adding dry ingredients and cooled Earl Grey milk to the butter mixture, beginning and ending with dry ingredients. Mix just until combined.