Note: If your ice cream machine requires pre-freezing, make sure to freeze in advance of making the custard base.
In a medium saucepan placed over medium heat, add the half-and-half and 1 ½ cups of the heavy cream. Add sugar and salt and whisk until dissolved.
While the cream mixture heats, add 2 egg yolks to the remaining ½ cup heavy cream, whisking to combine. When the cream is hot, slowly ladle some of the hot cream into the egg yolk mixture, whisking continuously. This process will temper the eggs so they don't scramble.
Then slowly pour the egg yolk mixture into the hot cream mixture, while whisking. Cook over medium-low heat until slightly thickened, being careful not to boil the cream mixture.
Strain the mixture into a heat-proof bowl. Whisk in the vanilla extract. Cover with plastic wrap, pressing the plastic wrap directly on top of the cream mixture. Refrigerate until completely chilled, approx 2 hours.
Transfer to an ice cream machine and churn until the mixture is the consistency of soft serve, approx. 45 mintues. Transfer to a freezer-safe container. Stir in peanut butter cups and Reese's pieces. Freeze until firm, approx 3-4 hours.
Notes
Yields 1 ½ quarts.
For an eggier-tasting custard base, add 1-3 extra egg yolks.
If you're not a fan of peanut butter cups, try Snickers, M&M's, or Heath Bars.