Heat a medium pot over medium heat. Add heavy cream and whole milk, sugar, cocoa powder, vanilla extract and salt. Cook, stirring frequently until warmed through. Add peanut butter and continue to stir until smooth and thick and the mixture reaches a simmer.
While the mixture is heating, in a medium glass bowl, whisk together the egg yolks. Now, temper the yolks. Slowly pour in ¼ cup of the simmering cream mixture into the egg yolks, whisking constantly to temper the eggs. Pour the heated egg yolks into the pot with the cream and milk batter and stir. Remove from heat.
Pour in the Bailey's and stir thoroughly. Add the chopped chocolate into the batter, mixing until chocolate has melted and mixture is smooth and thick.
Let mixture cool to room temperature, cover with plastic wrap, and let it cool in the fridge for at least eight hours.
When the mixture is ready, pour it into your ice cream maker and freezer according to manufacturers directions (usually about 20 minutes). Once the mixture begins to look thick and frozen, resembling typical ice cream, and a couple of minutes before instructions say the ice cream should be frozen, add in peanut butter cups.
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