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1
In the bowl of a standing electric mixer fitted with the whisk attachment, mix egg yolks and 1/4 cup sugar on high speed until pale and thick, 2 to 3 minutes.
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2
Prepare an ice-water bath.
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3
Bring milk, vanilla, and mint leaves just to a boil in a medium saucepan.
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4
Remove from heat.
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5
Whisk about one third of milk mixture into yolk mixture (this is called tempering, which keeps the yolks from curdling).
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6
Pour yolk mixture into pan with remaining milk mixture, and whisk to combine.
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7
Clip candy thermometer to side of pan.
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8
Cook over medium heat, stirring constantly, until mixture registers 185F.
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9
Remove from heat; strain through a fine sieve into a heatproof bowl (discard solids).
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10
Set bowl in ice bath, stirring mixture until cool.
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11
In another bowl of an electric mixture fitted with the paddle attachment, cream butter on medium-high speed until pale and fluffy.
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12
Beat in chilled egg-yolk mixture.
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13
Heat egg whites and remaining 1/4 cup sugar in the clean heatproof bowl of an electric mixer set over a pan of simmering water, whisking constantly by hand until mixture is warm to the touch and sugar has dissolved (the mixture should feel completely smooth when rubbed between your fingertips).
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14
Attach bowl to the mixer fitted with the clean whisk attachment; starting on low speed and gradually increasing to medium-high speed, whisk until stiff (but not dry) peaks form and mixture is completely cool (test by touching bottom of bowl), about 10 minutes.
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15
Add egg-white mixture to butter mixture; switch to the paddle attachment, and beat on medium-high speed until smooth.
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16
Beat in peppermint extract.
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17
Keep buttercream at room temperature if using the same day, or transfer to an airtight container and refrigerate up to 3 days or freeze up to 3 months.
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18
Before using, bring to room temperature, and beat with the paddle attachment on low speed until smooth again, about 5 minutes.
