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Place milk, cream, and 1 teaspoon of sugar in a small saucepan. Bring it to a gentle summer and then turn to low heat.
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In a heatproof bowl, add the remaining sugar and egg yolks. Whip until light, creamy, and pale yellow in color.
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Whisking constantly, slowly pour in the warmed milk and cream into the egg mixture.
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Strain the custard sauce through a fine mesh strainer and pour back into the saucepan.
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Over low heat, stir constantly until the custard starts to thicken. Do not raise the heat as you might end up curdling or burning the sauce.
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Once thickened, remove from the heat and pour through the strainer.
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Stir in the Bailey’s Irish Cream.
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Cover and place in warm spot while you make the lava cakes.