Heat the olive oil in a saucepan over medium heat. Saute the shallot for 3 minutes, add the garlic and saute for 30 more seconds.
Remove from heat and add the whiskey.
Add the brown sugar, ketchup, paprika, Worcestershire sauce, apple cider vinegar, tomato paste, and salt. Whisk to combine. Return to the heat.
Add the peaches and bring to a boil, then reduce heat to low and simmer for 20 minutes until thickened.
Remove from heat and puree with an immersion blender until smooth.
Use immediately or allow to cool completely before storing in an airtight container in the refrigerator.