Preheat your oven to 350°F (175°C) and generously grease a 2-quart soufflé dish or an 8x8-inch baking dish with butter.
Place the chopped carrots in a large pot, cover with water, and bring to a boil. Cook for 20-25 minutes until the carrots are very tender and can be easily pierced with a fork. Drain the carrots thoroughly in a colander.
Transfer the drained carrots to a food processor and process for 1-2 minutes until they form a completely smooth, lump-free puree. Let the puree cool for 5 minutes.
Add the granulated sugar, flour, baking powder, cinnamon, salt, eggs, melted butter, and vanilla extract to the food processor with the carrot puree. Process for another 1-2 minutes, pausing to scrape down the sides, until the batter is completely smooth and well combined.
Pour the batter into the prepared dish and bake for 45-55 minutes. The soufflé is done when the top is deep golden brown and the center is set with only a slight jiggle.
Let the soufflé rest for 10 minutes before serving. Dust the top lightly with powdered sugar just before serving.