Preheat the oven to 180⁰C. Grease five 300ml ramekins with 1 teaspoon of the softened butter. Place the ramekins in a glass baking dish large enough to hold them.
Combine the shredded carrots with water to just barely cover in a medium saucepan. Add 1 tablespoon of the sugar and the remaining 1 teaspoon softened butter. Cook over a medium heat until the carrots are soft, 2 to 4 minutes. Drain the carrots and transfer to a food processor. Puree until smooth.
Pour the carrot puree into a medium bowl. Stir in the melted butter and remaining ¼ cup sugar. Stir in the egg yolk. Stir in the flour, baking powder, and cinnamon until combined.
In a separate bowl, using an electric mixer, beat the egg white until soft peaks form. Gently fold the egg white into the carrot mixture. Spoon the carrot mixture into the ramekins.
Pour enough boiling water into the baking dish to come one-quarter of the way up the sides of the ramekins. Bake until the soufflés are set and bubbling, 30 to 35 minutes.
Remove the ramekins from the baking dish with metal tongs and transfer to a wire rack to cool for 5 minutes before serving. Serve in the ramekins.
Recipe by Whitney Miller.