Place a fine mesh strainer over a medium bowl that is set inside a larger bowl containing ice and water.
Whisk egg yolks and ¼ cup sugar together in a separate medium bowl. Set aside.
Heat cream, milk, remaining ½ cup sugar and salt in a saucepan over medium heat until steaming and just below a simmer.
Slowly and pouring in a steady stream, ladle about 1 cup of the warm cream mixture into the yolks, whisking constantly. Transfer the cream and egg mixture back to the saucepan with the remaining cream mixture. Cook over medium-low heat, whisking constantly, until mixture thickens and is just beginning to bubble.
Immediately strain custard through the prepared fine mesh strainer and add the vanilla. Allow it to cool in the bowl over the ice bath, stirring occasionally, until the mixture has come to room temperature. Cover and transfer the custard to the refrigerator to cool completely, at least 3 hours or up to 24 hours.
Transfer custard to an ice cream machine and churn according to manufacturer’s directions. Meanwhile, add the vodka to the Quick and Easy Peach Compote and stir to combine. Add compote mixture to the ice cream during the last few minutes of churning, making sure that it is distributed thoroughly. Transfer ice cream to an airtight container and freeze until ready to use.