Bring a pot of water to a boil if your peaches are firm. Score a small X in the bottom of each, drop them in for 30 to 45 seconds, then transfer to cold water. The skins will slip off easily.
If your peaches are soft and ripe, simply peel them with a swivel peeler or paring knife. Halve each peach, remove the pit, and dice the flesh into roughly 1/2-inch (1 cm) pieces. You should have about 5 to 6 cups of diced fruit.
Finely chop the red onion, mince the garlic, and grate the fresh ginger on a fine grater.
Set your heavy-bottomed pot over medium heat. Add the 1 cup (240 ml) apple cider vinegar, 1 cup (200 g) brown sugar, and 1/2 teaspoon salt. Stir until the sugar dissolves completely and the mixture comes to a gentle simmer. This usually takes 3 to 4 minutes.
Add the diced peaches, chopped onion, minced garlic, and grated ginger to the pot.
Stir in the 1/2 cup (75 g) golden raisins, 1 teaspoon mustard seeds, 1/2 teaspoon cinnamon, 1/4 teaspoon allspice, and 1/4 teaspoon red pepper flakes. Give everything a thorough stir so the spices are evenly distributed and the fruit is coated in the vinegar mixture.
Bring the pot back to a gentle simmer, then lower the heat so it bubbles steadily but not aggressively. Cook uncovered for 40 to 50 minutes, stirring every 5 to 10 minutes and scraping the bottom and corners of the pot each time.
As it cooks, the peaches will soften and break down, the liquid will darken to a deep amber, and the mixture will thicken. Toward the end, stir more often so nothing catches on the bottom.
The chutney is ready when a spoon dragged across the bottom of the pot leaves a trail that fills in slowly.
For a more precise check, drop a spoonful onto a plate chilled in the freezer. If it holds its shape and does not spread into a watery ring, it is done.
Remember that it will thicken further as it cools, so stop just before it looks as thick as you want it.
Turn off the heat and stir in the optional 1 tablespoon lemon juice for a final lift of brightness.
Taste carefully, since it is hot. Adjust with a pinch more salt or red pepper flakes if you like.
Ladle the hot chutney into clean glass jars, leaving about 1/2 inch (1 cm) of space at the top. Wipe the rims, seal with lids, and let the jars cool to room temperature on the counter.
Once cooled, transfer to the refrigerator. The flavor is good right away but noticeably better after a day or two.