Position a rack in the middle of the oven and preheat to 375. Butter the bottom and sides of a 2-quart souffle dish up to the top edge. Sprinkle with 1/4 cup parmesan and the cornmeal. Place in the freezer while you prepare the souffle.
Make the roux: Melt 6 tablespoons butter in a heavy-bottomed saucepan over medium heat and add the garlic. Stir in the flour, nutmeg and 2 teaspoons salt and cook, stirring, until the flour is cooked but not browned, about 2 minutes. Whisk in the milk and simmer, whisking constantly, until the mixture is as thick as pudding, about 5 minutes. Stir in the comte, emmentaler and 3/4 cup parmesan until melted, then remove from the heat. Stir in the 4 egg yolks one at a time. Transfer the mixture to a large bowl and stir to cool slightly.
Beat the 6 egg whites and lemon juice in a large bowl with a mixer until soft peaks form. Fold a quarter of the whites into the cheese base, then fold in the remaining whites.
Place the prepared souffle dish on a baking sheet, pour in the batter and smooth the top. Run your finger around the inside lip of the dish to push the batter away from the edge and create a ridge. Scatter the remaining 1/4 cup parmesan on top. Transfer to the oven and immediately reduce the temperature to 325. Bake until golden and puffed about 2 inches above the lip of the dish, about 35 minutes. Serve immediately with baguette slices and pate and/or apple butter, if desired.