Step 1Heat the oven to 350 degrees. Cut peaches in half and remove the pits, leaving the skin on. Cut the pineapple into 1-inch cubes.
Step 2Place the peaches cut side down on a sheet tray with either parchment or a silicone baking mat liner. Roast the peaches until the skin begins to crinkle, about 20 minutes. Remove the peach tray, and roast the pineapple cubes for 20 minutes.
Step 3Set the fruit aside to cool completely, then peel the peaches. Place the fruit in a food processor or blender and puree until smooth (this will need to be done in batches).
Step 4In a 6-quart (or larger) pot, combine the sugars and vinegar. Whisk the mixture over low heat until all of the sugar is dissolved. Add the mustard powder, onion powder, ginger powder and nutmeg and whisk to combine, then add the fruit puree and whisk until incorporated. Cook the mixture, uncovered, over low heat and whisk occasionally until thickened, about 25 minutes. The color will darken slightly. Season with the salt and set aside to cool completely.