Using a paring knife, scrape the seeds of the vanilla bean into the milk mixture, then add the pod. Heat the milk mixture over medium-low heat until simmering.
Do not bring to a boil. Remove from the heat, cover, and set aside for 1 hour to allow the vanilla to infuse into the liquid.
In another medium saucepan over medium heat, melt the butter. Stir in the brown sugar until it is completely dissolved. Set aside.
Add the milk mixture to the browned butter mixture and stir to thoroughly combine. Return the mixture to medium heat until it reaches 140°F on a kitchen thermometer.
Meanwhile, in the bowl of a stand mixer fitted with the whisk attachment, beat the egg yolks on medium speed for 2 minutes or until they turn pale yellow.
With the mixer running, gradually add one-third of the milk mixture to the egg yolks.
Add the remaining milk mixture to the bowl and whisk until blended.
Return the mixture to the saucepan and heat over medium-low heat, stirring constantly and scraping the bottom of the pan with a heatproof rubber spatula, until the mixture reaches 170°F and becomes a custard.
Pour the custard into a large bowl.
Stir in the rum or whiskey, vanilla extract, and cinnamon, if desired.
Bring to room temperature by setting the bowl in an ice bath: Fill a larger bowl with ice water and set the bowl of custard in it.
Then chill in the refrigerator until the custard reaches 40°F on a kitchen thermometer.
Remove the vanilla bean and transfer the custard to an ice cream maker.
Proceed according to the manufacturer's instructions.
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