For the cake: Preheat the oven to 350 degrees F. Butter a 9-by-13-inch cake pan.
Whisk together the flour, cocoa powder, baking soda and salt in a medium bowl and set aside.
Combine the butter and brown sugar together in a large bowl and beat with an electric mixer at medium-high speed until light and fluffy, about 3 minutes. Add the eggs 1 at a time, beating well after each addition. Beat in the vanilla. With the mixer on low, add the flour mixture in 3 batches, alternating with the red wine, beginning and ending with the flour, mixing until just incorporated.
Spoon the batter into the prepared baking pan and smooth the top with an offset spatula. Bake until a wooden skewer inserted into the center of the cake comes out clean, about 35 minutes. Cool completely on a rack.
For the buttercream: Place the butter in a large bowl and beat with a mixer on medium-high speed until smooth. Add the confectioners' sugar in 3 batches, beating until each batch is incorporated. After adding the last batch, continue to beat until very smooth and lightened, about 3 minutes. Add the vanilla and 1 tablespoon of the half-and-half and beat until incorporated. Add more half-and-half as needed to make the icing a smooth, spreadable consistency. Keep at room temperature until ready to use.
Spoon the buttercream onto the cake and smooth with an offset spatula. Cut the cake into squares and serve.
If you let this batter sit (before baking), it will discolor into an odd gray color, but it will turn into a beautiful chocolate brown in the oven so don't worry!