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Preheat the oven to 375?F with a rack in the middle of the oven. Butter an 8-cup/ 2-L soufflé mold and sprinkle with Parmigiano-Reggiano to coat completely all the way to the top. Shake any excess cheese out into a bowl. Put the molds in the freezer to chill.
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Melt the 1 tablespoon butter in a medium saucepan over low heat. Whisk in the flour, nutmeg, and salt; whisking constantly, cook the flour without browning, about 5 minutes. Whisk in the milk and garlic and continue to cook, whisking, at a low simmer until the mixture is smooth and thick like pudding, about 5 minutes.
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Stir in the Manchego and any Parmigiano-Reggiano left over from coating the molds and cook, stirring, until the cheese melts. Remove from the heat and stir in the egg yolks, one at a time. Continue stirring vigorously with a rubber spatula to cool.
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Whisk the egg whites and lemon juice in spotless bowl with an electric mixer on medium-high until they just hold a soft peak. The key is to not over-whip the whites, which would give your soufflé a cloudy instead of creamy consistency.
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Fold one-fourth of the egg whites into the cheese mixture with a rubber spatula, carefully turning the bowl and mixing gently until the whites are streaked throughout. Add the remaining whites and fold in but don’t overmix, which can deflate the whites.
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Transfer the batter to the chilled mold and scatter the remaining 2 tablespoons Parmigiano-Reggiano over the top. Place the dish on a baking sheet/tray and set in the oven, decrease the oven temperature to 325?F/ 165°C/gas 3, and bake until the soufflé is golden, puffed, and set but just a touch wobbly inside, 30 to 40 minutes. Serve immediately.