On a billboard in 24 Carrot Island, a Carrot Cake Model is shown, holding a piece of the cake on a plate.
While walking up to the Carrot Cake Factory, you're greeted by warning signs, toxic sludge, and this character on a billboard advertising the now-defunct carrot cake. The bill board itself reads "Carrot Cake; It's Delicious!". The character's identity is a mystery: it could be an employee of the factory, a hired model, or simply an artistic rendering of a man as were many people in advertisements at the time.
The Carrot Cake Model has a very similar facial hair style to Ambrose Burnside, an American Soldier.
The billboard itself is a reference to the advertisements in the time period 24 Carrot Island is set in. Whether he is a real person is unknown, as many advertisements at the time featured artistic renderings instead of photographs.