Combine the half-and-half and the whipping cream in a 4-quart saucepan and place over medium heat. Attach a frying or candy thermometer to inside of pan. Stirring occasionally, bring the mixture to 175ºF.
Remove from heat and add the sugar, preserves, vanilla bean and seeds, and kosher salt. Stir until the sugar has dissolved. Cover and steep for 20 minutes.
Remove the hull of the vanilla bean, if using, pour mixture into a container, and refrigerate, uncovered, until at least room temperature. Cover and refrigerate at least 6 hours and up to overnight to mellow flavors and texture.
Freeze mixture in ice cream maker according to manufacturer's instructions. Meanwhile, chop the browned peaches roughly. Once the mixture has reached a soft-serve consistency, add the peaches and continue to let it churn until just incorporated. Spoon the mixture into one or two lidded containers and harden in the freezer at least 2 hours before serving.