Prep the peaches by blanching them for 30 to 60 seconds in boiling water and then transferring to ice water to slip off skins, or use a swivel peeler for very ripe peaches. Halve, pit, and dice into 1/2-inch pieces.
Finely dice the red onion, grate the fresh ginger, and mince the garlic. Measure out all dry spices and set them aside together.
In a heavy-bottomed saucepan over medium heat, combine the apple cider vinegar and brown sugar, stirring until the sugar dissolves and the mixture simmers gently, about 2 to 3 minutes.
Reduce heat to medium-low and add the diced onion, grated ginger, and minced garlic to the simmering vinegar mixture. Cook for about 5 minutes, stirring occasionally, until the onion softens.
Add the diced peaches, golden raisins, cinnamon, cloves, nutmeg, red pepper flakes, and sea salt to the pot. Stir gently to coat everything evenly, then bring to a gentle simmer over medium heat.
Reduce heat to medium-low and cook uncovered for 30 to 35 minutes, stirring every 5 minutes, until the chutney thickens and holds its shape when a spoon is dragged across the bottom of the pot.
Remove from heat and taste. Adjust with additional brown sugar, vinegar, or red pepper flakes to your preference.
Cool the chutney in the pot for 15 to 20 minutes, then transfer to clean glass mason jars. Cool completely at room temperature with lids loosely placed, then seal and refrigerate.