Preheat your oven to 350°F (175°C) and generously grease a 2-quart soufflé dish or an 8x8-inch baking dish with butter or non-stick spray.
Place the peeled and chopped carrots in a large pot, cover with water, and bring to a boil. Cook for 20-25 minutes, or until the carrots are extremely tender and easily pierced with a fork. Drain the carrots thoroughly in a colander.
Transfer the drained, hot carrots to a food processor and process until completely smooth, scraping down the sides as needed. You should have about 2 ½ cups of carrot purée.
To the food processor, add the granulated sugar, flour, baking powder, vanilla extract, eggs, melted butter, milk, cinnamon, nutmeg, and salt. Process the mixture again for about 1 minute, or until all the ingredients are fully combined and the batter is silky smooth.
Pour the batter into the prepared baking dish and bake on the middle rack for 45-55 minutes. The soufflé is done when the top is deep golden brown, the edges are set, and the center jiggles only slightly when the dish is gently shaken.
Let the soufflé rest for 10-15 minutes before serving. It will deflate slightly as it cools. Dust the top lightly with powdered sugar just before serving.