While this might not be a traditional dessert recipe, Rhode Island's Coffee Milk certainly fits the bill for Sweet State of Mine: find something specific to each state that everyone there knows about, but that might be unfamiliar to people outside of the state.
Since I don't have a long list of ingredients or detailed recipe to share, I thought you might like to read more about Coffee Milk from Wikipedia:
"Coffee milk was introduced to Rhode Island sometime in the early 1930s. It came about from creative diner and drugstore operators trying to attract new customers with new and innovative drinks. One of these operators, the identity of whom has been lost to history, sweetened leftover coffee grounds with milk and sugar. This created a molasses-like extract that became popular. Coffee milk became a favorite among Rhode Islander and Southeastern Massachusetts residents, and created a demand for this coffee syrup. The demand was so great that, in 1993, it beat out Del's Lemonade as the official drink of Rhode Island.
In southeastern parts of the U.S. region of New England, it can be found in the dairy case of stores right next to other flavored milks such as chocolate, strawberry and vanilla, and is often found on the beverage menus of diners throughout the area.
The drink is difficult to find outside of the New England region, however, and travelers requesting it are often mistakenly served coffee with milk. One well-known brand of coffee syrup is "Autocrat", which also produces the Eclipse and CoffeeTime brands of coffee syrups, is based in Lincoln, Rhode Island.
Coffee milk is on tap in the dining halls of Brown University and the University of Rhode Island, confounding many of the students from outside the state.
Recently, the syrup became available as far south as Florida, but under different packaging. It is branded as "Coffee Time" syrup - still made by Autocrat in Rhode Island."
but, I wanted the original, real deal Rhode Island coffee syrup - Autocrat!
I found a source online, placed my order and a few days later, had my own bottle to make Rhode Island's Official state drink!