Puree the peaches in a food processor until smooth. You should have 3 cups. Set aside.
Heat a Dutch oven or large saucepan over medium-low heat. Heat the vegetable oil, then add the onions and garlic.
Cover and cook, stirring occasionally, for 10 minutes. Remove from the heat.
Stir in the peach puree, brown sugar, vinegar, bourbon, Worcestershire, and red pepper flakes.
Carefully return the pot to the heat and bring the mixture to a boil. Reduce the heat to low and simmer, uncovered, stirring occasionally, for 30 to 40 minutes, until thick.
Remove from the heat.3.Stir in the mustard and salt. Let cool, then transfer to an airtight container.
If you’re making this ahead, transfer it to a nonreactive container and refrigerate for up to 1 month.
The sauce will also keep in the freezer for up to 1 year.