Preheat the oven to 350 F. In a large bowl, whisk together flour, sugar, salt, baking soda, and baking powder. Add in the eggs, milk, vegetable oil, and vanilla extract, mix until smooth.
Fold in the crushed Oreo cookies. Pour the cake batter into a greased baking dish. Bake for 40-45 minutes. Let cool completely.
For the frosting, in a large bowl, mix butter with powdered sugar, vanilla extract, and milk until combined. Fold in the crushed Oreo cookies.
Frost cake with the frosting.