In a large, non-reactive, saucepan over medium-low heat, melt the butter. Add the onions, cook until softened but not browned, about 10 minutes. Add the apple and continue cooking until cooked, but still slightly firm, about 10 minutes more.
Sift the flour over the onions. Add the nutmeg. Cook and stir with a wooden spoon until the mixture is lightly browned and fragrant, about 4 to 5 minutes. Add the Calvados, if using, and cook to reduce by three-quarters.
Gradually whisk in the broth until well blended. Bring to a boil, reduce heat, cover, and simmer, stirring occasionally for 10 minutes. Add the milk, return to just a boil, whisk in cheeses until completely melted. Season with pepper to taste.
Serve hot, with crumbled bacon on top, and a crusty bread and chutney on the side.
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