Preheat the oven to 350F. Butter a large soufflé dish and roll ¼ cup of granulated sugar throughout the dish, making sure to cover all the interior surfaces. Set aside the prepared soufflé dish.
Bring 1 cup of the milk to just steaming in a medium saucepan set over low-medium heat. Stir together 1/3 cup granulated sugar, 1/3 cup all-purpose flour, and the remaining 1/3 cup milk until it forms a smooth batter.
Slowly whisk half of the hot milk into the batter, making sure to combine the ingredients until they are completely smooth. Add the tempered batter back to the hot milk in the pan and bring the mixture to a simmer, stirring constantly. Stir and cook the mixture until it has thickened, for about 1 minute. Stir the butter into the mixture and allow it to cool at room temperature for 10 minutes. Stir in the vanilla extract.
In a separate bowl, beat the egg whites on medium high speed until they become foamy, and then add the remaining 2 tablespoons sugar. Continue beating the egg whites on high speed until they hold stiff glossy peaks.
Gently stir 1/3 of the egg whites into the vanilla mixture, then carefully fold in the remaining whipped egg whites. The vanilla mixture should be evenly colored and light and bubbly, without egg white streaks or marbling.
Spoon the soufflé mixture into the prepared dish and allow it to rest, covered, for up to 30 minutes or bake right away for 25 to 30 minutes (slightly longer at high altitudes) until the soufflé has risen with a crusty exterior. Serve the soufflé with a dusting powdered sugar and a few plump berries, if desired.