Bring butter, walnut milk and sugar to a boil in a saucepan. Add flour and toast over low heat until dough comes to a smooth ball, stirring constantly, being cautious not to scald.
Transfer to stand mixer with paddle attachment and slowly add eggs, one at a time, adding each after previous egg is fully emulsified. Transfer to a pastry bag with a round medium-sized tip. Pipe 1-inch mounds onto a lined sheet tray and brush with egg wash.
Bake in a 315° F convection oven. After 14 minutes, rotate and finish cooking. When finished, profiteroles should have tripled in size and be very light and airy to the touch.
To serve, reheat profiteroles in a 350° F oven for 1 minute. Cut top off and fill with pastry cream and place top back on.
WALNUT MILK
Toast walnuts in a 325° F oven until nicely browned and aromatic. Combine walnuts and water in a saucepan and let steep over low heat for 20 minutes.
Purée in a blender until a smooth milk-like consistency is achieved, then strain through a fine-mesh strainer. Reserve until needed.
PASTRY CREAM
Bring milk and 30 grams sugar to a boil. Temper in egg yolks and eggs, remaining sugar, cornstarch and vanilla and cook over low heat until custardy, then fold in butter.
Transfer to a bowl and cover surface with plastic wrap so pastry cream doesn’t develop a skin. Let cool for at least 1 hour and reserve until needed.