In a medium sauce pot, combine heavy cream, milk and 1 tablespoon sugar to a boil. Remove from heat.
In a large bowl, whisk together remaining 1/2 cup sugar and egg yolks. Temper hot milk into sugar yolk mixture. Slowly add hot milk about 1/4 cup at a time, whisking to distribute heat. Once all the milk has been added, transfer mixture back into the pot.
Place pot over medium-low heat. Stir until mixture reaches nappé consistency, or 180 degrees F on a kitchen thermometer. Let mixture sit at 180-185 degrees for 5 minutes to pasteurize egg yolks. Add peanut butter and salt. Stir to combine until peanut butter has dissolved. Let sit for 5-10 minutes and allow to cool slightly.
Strain mixture and transfer to an airtight container. Let mature in the fridge overnight.
Freeze peanut butter mixture in ice cream maker according to your unit's instructions.** Once the volume has increased by half and reached a soft serve consistency, transfer mixture into an airtight container and let harden in the freezer for at least 30 minutes before serving.