Preheat the oven to 350°F. Coat the inside of a 2- to 3-quart baking dish with butter, then add cornmeal to coat. Place in a larger deep baking dish.
In a heavy-bottomed saucepan, combine the milk and salt. Warm over medium heat, stirring frequently, until small bubbles appear all around the outside of the pan (it should register 180–185°F).
Reduce the heat to low and whisk in the grits. Be careful to add the grits gradually so that they evenly incorporate. Continue to cook, stirring regularly, until thickened and cooked thoroughly, about 20 minutes.
Place the egg yolks in a heatproof bowl. As you whisk, add a small ladleful of the grits mixture into the yolks to temper them. Once incorporated, whisk the tempered yolks into the saucepan.
Fold in the cheeses, onion puree, and soft butter.
Season generously with black pepper and nutmeg, and add salt to taste. Fold in parsley and thyme.
In a large mixing bowl or the bowl of a stand mixer fitted with the whisk, whip the egg whites until they form medium-stiff peaks. Add the whites in three additions, folding very gently after each addition.
Ladle the soufflé into the prepared dish, leaving a bit of space at the top for them to rise. Carefully pour boiling water into the larger baking dish so it comes about halfway up the soufflé dish, being careful not to let it splash.
Bake, uncovered, for 15 minutes. Rotate the pan halfway, then continue to bake for about 15 minutes longer.
Carefully pull the pans from the oven and transfer the soufflé dish to a wire rack to cool slightly. To serve, use a butter knife to loosen the sides, then invert onto a plate. Serve right away.
Note: To make the Vidalia onion puree, place whole Vidalia onions on a sheet tray. Roast at 375°F for 40 minutes, or until very soft. Let cool completely. Remove the peels, puree, and store in the refrigerator.
