Preheat oven to 350 degrees F (175 degrees C). Grease two 8-inch round cake pans.
Mix milk, almond extract, salt, and vanilla extract together in a small bowl.
Combine sugar and butter in a large bowl; beat with an electric mixer until creamy and smooth. Beat in eggs one at a time. Mix in pistachio nuts. Add flour to the creamed butter mixture alternately with the milk mixture, stirring batter well after each addition.
Mix vinegar and baking soda together in a small bowl. Fold into the batter. Divide batter between the prepared cake pans.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 30 minutes. Cool in the pans for 10 minutes. Invert onto a wire rack to cool completely, about 20 minutes.
Spread white frosting between cake layers. Stack layers; frost top and sides of cake.