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Add butter to a bowl, and microwave until melted. Allow to cool a few minutes.
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Meanwhile, combine egg yolks, lemon juice and water in a small pan over low heat. Whisk constantly, until the mixture gets foamy, then smooth, and turns a pale yellow. This should take about 5 minutes.
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Slowly, very slowly, add butter to egg mixture, whisky constantly. Add no more than a teaspoon of butter at a time. This is a slow process - but totally worth it! Continue adding and vigorously whisking until butter is fully incorporated, and hollandaise sauce is smooth. Sprinkle in remaining Parmesan cheese, salt and pepper, and whisk until smooth.
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Serve stuffed artichokes with hollandaise sauce, and enjoy within the hour!