For the Rub: Combine all ingredients and grind in coffee grinder.
For the Sauce: Combine all of the ingredients in a nonreactive saucepan and slowly bring to a boil over medium-high heat. Reduce the heat to medium-low and gently simmer until dark, thick, and richly flavored, 10 to 15 minutes. Transfer the sauce to a clean jar and store in the refrigerator. It will keep for several months.
Preheat grill for medium heat and lightly oil the grate. Lightly Season chicken breast halves with sea salt and black pepper.
Stir peach preserves, olive oil, soy sauce, garlic, and mustard in a bowl; season with salt and black pepper. Reserve about 1/2 cup peach sauce.
Place chicken on preheated grill; cook until golden brown, 6 to 7 minutes, then flip chicken. Continue cooking for 5 to 6 minutes. Brush both sides of the chicken with peach sauce. Cook until no longer pink in the center and the juices run clear, 4 to 5 more minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).
Arrange peach halves cut side down on the grill. Grill for 2 minutes, flip, and sprinkle with brown sugar and cinnamon and brush with reserved 1/2 cup peach sauce .
Continue to grill until peaches are tender, 3 to 4 minutes more.