Combine the egg yolks and 1/4 cup sugar in a mixer bowl; whisk on high speed until pale and thickened, 2 to 3 minutes.
Bring the milk to a boil in a medium saucepan; remove from heat. Whisk about one-third of the milk into the yolk mixture. Pour the mixture back into the pan with the remaining milk; whisk to combine. Cook over medium heat, stirring constantly, until the mixture registers 185 degrees on an instant-read thermometer. Remove from heat; strain. Refrigerate until cool.
Put the butter into a clean mixer bowl; beat on medium-high speed until pale and fluffy. Mix in the chilled custard and the pistachio paste; set aside.
Heat the egg whites and remaining 1/2 cup sugar in a clean heatproof mixer bowl set over a pan of simmering water, whisking constantly, until sugar has dissolved. Attach bowl to mixer, and whisk on high speed until stiff peaks form.
Add the egg-white mixture to the butter mixture; beat on medium-high speed until smooth.
Amounts for filling and frosting: The amounts provided are for a standard two-layer 4-inch-tall tier, filled with a 1/4-inch-thick coating of buttercream between the layers. For 6-inch: 3/4 cup to fill, 1 1/2 cups to frost; 8-inch: 1 1/4 cups to fill, 2 cups to frost; 10-inch: 2 1/2 cups to fill, 3 1/2 cups to frost; 12-inch: 3 cups to fill, 4 1/4 cups to frost. (Note: Many cake makers will split the two cake layers in half horizontally and spread filling between all four resulting layers; if this is your plan, triple the filling amount.)
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