Cut butter into pieces and mash with a spatula until the consistency resembles mayonnaise.

In a small bowl, whisk the egg yolks, then add the granulated sugar and whisk until the mixture lightens to an off-white and you can no longer see the granules of sugar. Add the milk, and whisk to combine.

Pour the egg mixture into a small saucepan and heat over low heat, whisking frequently to ensure that the mixture does not curdle or scorch. Cook until the mixture becomes thick and custardy, like pudding.

Pour the egg mixture back into its bowl and whisk constantly until it returns to room temperature. Whisk in the butter in three batches, add the vanilla, and stir until smooth and all ingredients are fully combined. Pipe or spread onto one macaron half and sandwich between the other.

Makes enough for 2 dozen macarons.