Step 1

Combine sugar, 1/4 cup water, and corn syrup in a small saucepan, making sure to wipe down the sides of the pan so no crystals form. Bring mixture to a low boil over medium. Boil, undisturbed, until golden, 6 to 8 minutes. Continue cooking, gently swirling mixture occasionally in a circular motion (do not stir), until mixture turns a deep amber color, 2 to 4 minutes. Remove from heat. Carefully whisk in cream. (Caramel will seize but then sugar crystals will dissolve.) Add butter; whisk until melted, about 1 minute. Stir in bourbon and salt; whisk again. Let cool to room temperature, about 1 hour. Cooled caramel can be stored in a resealable container in refrigerator up to 2 days; let come to room temperature before using, about 30 minutes.

Step 2

Remove peel from 1 lemon; set peel aside. Juice peeled lemon to yield 1/4 cup juice in a small bowl; if needed, juice remaining lemon to reach 1/4 cup juice total. Discard seeds. Cover juice, and place in refrigerator until ready to use. Stir together cream and reserved lemon peel in a resealable container. Let steep in refrigerator until flavors meld, at least 24 hours or up to 48 hours.

Step 3

Stir together peaches and sugar in a small saucepan. Let stand, stirring occasionally, until juices release, 10 to 15 minutes. Cook over medium, stirring often, until sugar is dissolved and mixture begins to boil, about 5 minutes. Remove from heat; let cool to room temperature, about 1 hour.

Step 4

Pour lemon peel–cream mixture through a strainer into a medium bowl; discard peel. Transfer infused lemon cream to a blender; add cooled peach mixture, crème fraîche, reserved lemon juice, and salt. Pulse mixture until almost smooth but slightly chunky, about 10 pulses. Transfer mixture to a large resealable container; chill in refrigerator until cold, at least 4 hours or up to 12 hours.

Step 5

Working in batches if needed, pour chilled peach mixture into frozen freezer bowl of an ice cream maker; proceed according to manufacturer's instructions. When mixture reaches soft-serve consistency and with ice cream maker running, gradually add 1 cup caramel to ice cream to create a swirl. Serve immediately for a soft-serve consistency, or transfer to a shallow airtight container, and freeze until firm, about 3 hours. Store ice cream in an airtight container in freezer up to 3 weeks.