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In a small saucepan, heat the oil over medium heat. Add the onion, cover, and cook until soft, about 5 minutes. Stir in the broth and nutritional yeast, turmeric, salt and pepper, and simmer stirring occasionally, until the mixture starts to bubble. Whisk in the cornstarch and cook, whisking, for 1 to 2 minutes to thicken.
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Transfer the mixture to a blender or food processor and blend until smooth. Add the lemon juice, mustard, and milk, and blend for a few seconds. Taste, adjusting the seasonings if necessary. Return the sauce to the saucepan and heat over low heat, stirring, until hot.
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If not using right away, cool the sauce to room temperature, then transfer it to a container, cover and refrigerate until needed. Properly stored, the sauce will keep for 2 to 3 days. Reheat the sauce in a saucepan over low heat.