Heat olive oil in a saucepan over medium heat. Add minced garlic and chopped onion. Sauté until translucent.
Stir in chopped peaches, brown sugar, apple cider vinegar, ground ginger, ground cinnamon, and a pinch of salt.
Bring the mixture to a simmer, then reduce the heat to low. Let it cook uncovered for about 40-45 minutes, stirring occasionally, until the chutney thickens.
Once thickened, remove from heat and let it cool completely.
Transfer the chutney into sterilized jars and seal tightly. Store in the refrigerator.