Step 1

Preheat the oven to 350 degrees F.

Step 2

Grease a 9-inch square baking dish or an 11x7-inch baking pan.

Step 3

In a large bowl, add the water, the mayonnaise, and the vanilla and stir to combine.

Step 4

In a second large bowl, add the flour, the sugar, the cocoa, and the baking soda and stir to combine.

Step 5

Use an electric hand mixer to gradually beat the flour mixture into the mayonnaise mixture until it is blended.

Step 6

Evenly pour the cake batter into the prepared baking pan.

Step 7

Bake the cake until a toothpick inserted into the center comes out clean, about 30-35 minutes.

Step 8

Transfer the baking pan to a wire rack and let the cake cool completely.

Step 9

In a small saucepan over medium heat, add the brown sugar and the butter and cook, while stirring, until it is bubbly.

Step 10

Transfer the saucepan from the heat, then stir the milk into the brown sugar mixture.

Step 11

Gradually add the confectioners' sugar to the frosting mixture and use a clean electric hand mixer to beat until it is smooth.

Step 12

Evenly spread the frosting over the top of the cooled cake.

Step 13

Slice and serve.