In Batter Bowl #1, whisk together the eggs yolks and 6 tbsp of the granulated sugar until thick and slightly foamy, about 30 seconds. Set aside.
In the large saucepan, whisk together the milk, cream, and salt. The mixture will be slightly thick from the cream.
Take macerated peaches and smash lightly with a fork or potato masher so pieces are smaller. Pour the peaches and all the syrupy liquid into the saucepan with the milk mixture.
Place the saucepan over medium-high heat and warm the mixture up until it’s just starting to simmer; this means tiny bubbles should just start appearing around the edges of the saucepan. The mixture will de-thicken right before it begins to simmer. This will take 10-15 minutes.
Turn off the heat and remove the saucepan from stove to Potholder #2, next to Batter Bowl #1 containing the egg yolks.
Use the soup ladle to carefully scoop out some hot liquid from the saucepan, being careful to avoid the peaches. Whisk the egg yolks to break them up a bit, then slowly stream the hot liquid into the egg yolks, whisking briskly the entire time to prevent the egg yolks from curdling. Once the first scoop is thoroughly whisked in, repeat process two more times, whisking the entire time to prevent the egg yolks from curdling.
Place the fine mesh strainer over the top of Batter Bowl #1 containing the tempered yolks. Pour the remaining milk mixture through the strainer into Bowl #1, catching the peaches in the strainer.
Remove strainer and carefully spoon hot peaches into the food processor. Blitz until smooth.
Place empty strainer on Batter Bowl #2.
Carefully pour the blended peaches into Batter Bowl #1, whisking to combine with the egg yolk mixture.
Pour the egg yolk mixture from Bowl #1 back into the saucepan. All ingredients should now be in the saucepan.
Return the saucepan to the stove on medium heat. While continuously stirring with a rubber spatula, heat the mixture until it thickens and thickly coats the back of the spatula, about 5 minutes. When it’s ready, you should be able to create a clear trail when you run your finger on the back of the spatula.
Carefully pour the hot liquid through the fine mesh strainer placed over Batter Bowl #2. Let blended peaches sit in the strainer and push them with a spatula to make sure all the liquid strains into Bowl #2. Then discard blended peaches.
Place Batter Bowl #2 gently into Ice Water Bowl, making sure that the bottom of Batter Bowl #2 touches the ice water but does not allow any ice water to get into the bowl.
Stir ice cream base in Bowl #2 occasionally until the base has cooled, about 40 minutes.
Once ice cream base is cooled, cover Bowl #2 with plastic wrap and refrigerate for 12-24 hours.