Cut 4 medium peaches in half and remove pits.
Place cut-side down on a parchment-lined baking sheet.
Preheat broiler and position rack 6 inches from heat.
Broil for 1-2 minutes until skins blister slightly.
Remove and let cool for 1 minute, then peel skins off easily with your fingers.
Slice peeled peach halves into 1/4-inch thick pieces (325g total).
In a medium saucepan, combine sliced peaches (fresh or frozen), granulated sugar, cornstarch, lemon juice, vanilla extract, ground ginger, cinnamon, nutmeg, and salt.
Cook over medium heat, stirring gently, for 10-12 minutes until peaches begin to soften and release their juices. If using frozen, cooking time will be less.
Continue cooking for 2-3 more minutes until mixture thickens and becomes glossy.
Most peaches should soften but some can remain slightly firm for texture.
Remove from heat and let cool completely (at least 45 minutes). Cover with plastic wrap and refrigerate until cold for faster cooling.