Add all of the sauce ingredients to a medium saucepan. Place on the stovetop over medium heat and heat until the mixture bubbles. Reduce the heat and simmer, stirring occasionally, for 10-15 minutes.
Use a potato masher or fork to break up the peach chunks a bit, then continue simmering the sauce for another 10 minutes or so.
Remove the sauce to a 2-cup measuring cup and use an immersion blender to smooth the sauce (or transfer to a small food processor to blend).
Brush the sauce onto chicken or pork on the BBQ or a hot grill pan in the oven. If using the oven, turn the broiler on for a few minutes at the end of cooking to brown up the sauce a bit. I like to brush a bit more sauce on top of the meat before serving and/or pass additional sauce at the table.
Notes
Note 1: If you don't have tarragon (or don't enjoy the flavour), you can substitute dried or fresh thyme using half the quantity specified for the tarragon. A bit of fresh or dried basil would also work in this sauce.Makes approximately 1 1/4 cups of sauce.Store leftover peach BBQ sauce in the refrigerator for up to 2 weeks or freeze up to 3 months.Be sure to read the notes above this recipe card for more tips on making this recipe. You'll also find step-by-step photos that you might find helpful.