Add peaches, tomato paste, vinegar, maple syrup, ginger, mustard, garlic, oregano, smoked paprika, pepper, and 10 grinds salt to a food processor. Blend until well combined into a thick sauce, about 1 minute. It’s okay if some some flecks of ginger remain.
Pour the sauce into an 8-inch frying pan. Heat to a soft boil over medium heat, about 3 minutes. Reduce heat and simmer for 4 minutes more. Remove from heat.
Use right away or cool on the countertop, pour into a container, label, and refrigerate.