Peach Salsa: Preheat grill or grill pan to medium-high heat (about 400–450°F.) Generously oil the grill—don’t skip this step (see note 1). Halve the peaches and remove the pits. Lightly brush the sides and skins with oil.Grill peaches until tender and lightly charred but still firm enough to chop, about 4–5 minutes total, flipping halfway.Chop peaches into small, even pieces and add to a medium bowl. Add diced red pepper, diced jalapeño, diced red onion, 1 tablespoon lime juice, coarsely chopped cilantro, chili powder, and salt and pepper (or to taste). Gently toss and taste. Adjust to preference (more salt/chili powder/lime juice). Refrigerate until ready to eat. Toss again right before adding.
Glaze: In a large bowl, combine peach preserves, olive oil, soy sauce, mustard, garlic, and jalapeño. Season to taste with the salt and pepper. Set aside 1/3 cup of this glaze for the end of the recipe.
Halve the chicken breast(s) horizontally and pound the pieces to even thickness (not super-flat, just even so it will cook evenly). Drizzle each side with olive oil, salt, and pepper. Flip pieces and repeat—oil, salt, pepper, seasoning. Place prepared chicken on the grill. Grill 8–10 minutes, flipping once halfway, and brushing generously with the peach glaze (not the 1/3 cup that you set aside), or until chicken juices run clear and internal temperature is 160–165°F. (carryover heat will take the chicken to 165°F). Tent chicken with foil and let stand 5–10 minutes.
Brush the remaining 1/3 cup of the peach glaze over the cooked chicken and top with peach salsa (taste again before adding on top of the chicken and add any additional salt/pepper). Enjoy while hot.
Notes
Note 1: To oil the grill, I drench a rolled-up paper towel in vegetable oil and, holding it with tongs, rub it over the grill grates. For a grill pan, brush 1 tablespoon oil over the pan.Storage: Store chicken and salsa separately. Refrigerate chicken for 4 days and salsa for 2. Reheat chicken; serve salsa chilled or room temp.