Preheat the oven to 350 degrees F (175 degrees C). Grease two 9-inch round pans.

In a large bowl, beat together 1 1/2 cups sugar and shortening with an electric mixer until light and fluffy. Add eggs one at a time, beating well after each addition.

Make a paste with red food coloring and cocoa, then add it to the creamed mixture.

In a separate small bowl, mix together buttermilk, salt, and 1 teaspoon vanilla extract. Add flour to the creamed mixture, alternating with buttermilk mixture, mixing just until incorporated.

In another small bowl, mix vinegar and baking soda together, then gently fold it into the cake batter. Pour the batter into the prepared pans.

Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 30 minutes. Cool the cakes on a wire rack for 5 minutes, then carefully invert them onto a serving plate or cooling rack. Let them cool completely, about 30 minutes.

While the cakes are cooling, make the icing: Heat milk and flour in a saucepan over low heat, stirring constantly, until thick. Set aside to cool completely.

In a large bowl, beat together sugar, butter, and vanilla extract until light and fluffy. Add the cooled flour mixture and beat until the frosting is a good spreading consistency.

Frost the cooled cake layers with the icing when they are completely cool.