Preheat oven to 350°F. Grease cake pans and line with parchment paper; set aside.
In a small bowl, combine egg replacer and water and set aside. In another bowl, sift together flour, baking powder and salt.
Cream together butter and sugar until very light and fluffy. Add egg replacer mixture and mix thoroughly. Add the flour mixture followed by the milk and vanilla and mix well after each addition.
Portion the batter into the prepared pans and spread evenly. Bake until a toothpick inserted in the center comes out clean, 25-30 minutes.
Let cool for about 20 minutes, then remove from pans to cool thoroughly.