Fat Tuesday got its name because it's supposed to be the last day to eat fat and other decadent ingredients before the asceticism of Lent. Some places still have pancake races and pancake dinners as that is one way to use up several of the disapproved-in-Lent ingredients. Other food-related traditions include King's Cake and paczki (jelly- or cream-filled donuts).
If you want to celebrate and don't have much time to bake, picking up a cake or some paczki at a bakery is an easy answer. For those who still want to impress with a baked-myself treat, Serious Eats offers a recipe for a Tie-Dyed Mardi Gras Cake recipe that might be just the thing. Although it is shown as a layer cake, you can bake it in a single large pan to make it even easier.
Bake one this weekend, and finish the last slices after Hartford's own Mardi Gras parade, which starts at 5:15pm on March 4th (what a perfect day for a parade!) at a to-be-named location. You can check with the Hartford Hot Several for additional details; Pratt Street seems likely.