Position a rack in the upper third of the oven and preheat to 450°F (230°C). Place a colander in a large bowl. Line 2 rimmed baking sheets with aluminum foil and top with the peppers. Roast, turning as needed, until evenly charred and blistered, 25–30 minutes. Transfer to the colander, cover, and let stand for 3 hours.
Have ready hot, sterilized jars and their lids.
Working over the colander, peel and seed the peppers, capturing the juice in the bowl and placing the cleaned peppers in a second colander over a bowl. Cut the peppers into long strips 2 inches (5 cm) wide. Measure 3 packed cups (30 oz/940 g); reserve the remainder for another use. In a bowl, mix the peppers, ginger, and garlic. Measure the juice from both bowls; you should have about 1½ cups (12 fl oz/375 ml). Pour into a large nonreactive saucepan, and add twice the amount of vinegar. Stir in the sugar and salt and bring to a boil over medium-high heat.
Divide the peppers evenly among the jars. Ladle the hot brine into the jars, leaving ½ inch (12 mm) of headspace. Remove any air bubbles and adjust the headspace, if necessary. Wipe the rims clean and seal tightly with the lids.
Process the jars for 10 minutes in a boiling-water bath (for detailed instructions, including cooling and testing seals, Canning Step by Step). Let the jars stand undisturbed for 24 hours and then set them aside for 2 weeks for the flavors to develop. The sealed jars can be stored in a cool, dark place for up to 1 year. If a seal has failed, store the jar in the refrigerator for up to 1 week.