In a small saucepan, combine butter, 3 tablespoons (45 grams) water, milk, sugar, vanilla, and salt. Cook over medium heat until butter is melted and mixture begins to boil. Add flour, stirring vigorously with a wooden spoon. Cook, stirring constantly, until dough pulls away from sides of pan and forms a ball and a film is left on bottom of pan, 1 to 2 minutes. Remove from heat.

Transfer mixture to a medium bowl. Beat with a mixer at low speed until dough is warm to the touch, about 1 minute. Add eggs, one at a time, beating until combined after each addition. (Batter should be shiny and slowly move back together when a spatula is dragged through it; after being stirred a bit, dough should also fall off mixer attachments or spoon so excess is left hanging in a V shape.) Cover and let stand at room temperature until ready to use.