Cut each slice of Texas toast into four sticks. Set aside.
In a large bowl, whisk together the eggs, heavy cream, cinnamon, sugar and vanilla. Dip each piece of bread in the egg mixture, turning to coat it on all sides so that it's well-saturated with the custard.
Shake off any excess and place the coated bread on a large plate or baking dish. Repeat the dipping process with the remaining pieces of bread.
Heat a large sauté pan over medium heat and add 2 to 3 tablespoons of butter. Once the butter has melted, place several of the coated sticks in a single layer in the pan. (Do not overcrowd the pan.) Cook until golden brown on one side then flip and continue cooking until the sticks are golden brown and slightly crisped on all edges.
Serve immediately with maple syrup for dipping.