In a saucepan, heat olive oil over medium heat.
Add onion and cook until soft and translucent, about 5 minutes.
Add garlic and peaches and cook for another 2 minutes, until fragrant.
Reduce the heat to low and add the apple cider vinegar, tomato paste, lemon juice, paprika, mustard, salt and pepper.
Stir well until the mixture is relatively smooth. Simmer for 5 to 7 minutes, until the mixture has thickened.
Remove from heat. Using a want blender, blend until smooth (or pour into a blender or food processor).