Prepare an ice bath by filling a large bowl with a handful of ice cubes and adding a few splashes of water. Set a slightly smaller bowl inside this bowl and place a sieve or strainer inside. Set aside.
Heat the cream and sugar over medium heat in a saucepan until it reaches a slight simmer and the sugar dissolves. Remove from heat.
Whisk the egg yolks together in a medium mixing bowl. Temper the cream mixture by adding 1/4 c. of the warm cream mixture to the egg yolks, whisking the entire time. Add the remainder of the cream and whisk.
Return mixture back to the medium saucepan over low heat. Cook, stirring constantly, until 170-175 degrees F and the mixture thickens enough to coat the back of a spoon.
Pour the mixture through the sieve into the small bowl of your ice bath. Add the honey, vanilla, and buttermilk. Stir constantly until the mixture becomes room temperature.
Cover the bowl with plastic wrap and transfer it to the fridge for at least 4 hours, until very cold.
Make the peach swirl: Bring a medium pot of water to a simmer. Add the peaches and blanch for 1-2 minutes. Remove the peaches and let cool slightly. Use a paring knife to remove the skins from the peaches. Chop the peaches and discard the pits. Add the chopped peaches, sugar and salt to a medium saucepan and cook over medium heat for 10-15 minutes, until bubbling and peaches are nearly broken down. Turn off the heat and let cool slightly.
Transfer the peach mixture to a food processor or blender and pulse until pureed, about 10 seconds. (Make sure to allow a bit of hot air to escape from your blender to avoid a peach explosion!)
Transfer to a bowl and allow to come to room temperature.
Churn the ice cream mixture according to your ice cream maker’s instructions. Transfer 1/3 of the mixture to a freezer-safe container, drizzle with about one-third of the peach puree. Repeat with the remaining ice cream and peach puree. Make sure the peach puree isn’t too thick, as it tends to freeze with a crunchy ‘popsicle’ texture. Freeze until firm, at least 8 hours.