How to Make It
Cook blueberries, 1/4 cup sugar, and lemon juice in a medium-size, heavy-bottomed saucepan over medium-high, stirring occasionally, until berries begin to burst and liquid begins to thicken, 8 to 10 minutes. Remove from heat, and let cool 30 minutes. Transfer to a bowl. Cover and chill until completely cool, at least 1 hour or until ready to use (up to 1 week).
Process chopped peaches in a food processor until almost smooth (applesauce consistency), leaving a few chunky bits, about 30 seconds. Set aside.
Stir together heavy cream, whole milk, corn syrup, salt, and remaining 1/2 cup sugar in a medium saucepan, and cook over medium, stirring occasionally, just until mixture begins to simmer (bubbles begin to form around the outside edge of pan), 5 to 6 minutes.
Meanwhile, whisk together egg yolks and vanilla in a large bowl. While whisking yolk mixture constantly, carefully ladle about 1 cup hot cream mixture into yolk mixture; continue whisking until cream mixture is fully incorporated. Carefully whisk in remaining hot cream mixture.
Pour custard mixture back into saucepan, and cook over medium-high, whisking constantly, until mixture begins to thicken and coats the back of a spoon, 6 to 8 minutes. Remove from heat, and let cool 10 minutes.
Stir bourbon and pureed peaches into custard. Pour custard mixture into a gallon-size ziplock plastic freezer bag. Seal bag, and place in an ice bath. Let stand until mixture is completely cool, about 30 minutes.
Pour mixture into a 1 1/2-quart electric ice cream maker, and proceed according to manufacturer’s instructions. (Instructions and times may vary.) Transfer to an airtight, freezer-safe container; freeze until slightly firm, about 30 minutes. Dollop blueberry mixture over ice cream, and swirl with a spoon. Cover and freeze until firm, at least 4 hours or up to overnight.