Prep jars. Make sure the jars are clean and heated in the oven at 200°F or in a pot of hot water. Then, heat the rings and lids in a small pan of hot water. Fill your canner with water and bring it to a boil.
Prep your jalapeños. Get your peppers and if you have a scale, weigh 3 pounds (about 8 cups of sliced jalapeños). Don't forget to wear gloves and start slicing the peppers by hand.
Make the syrup. Combine the vinegar, sugar, cinnamon, turmeric, and ginger in a large stockpot or high-sided sauté pan. Bring the mixture to a boil over medium-high heat. Once boiling, reduce the heat to low and let it simmer until the liquid turns into a sticky syrup for approximately 5 to 7 minutes.
Cook the jalapeños in the hot syrup. Increase the heat to medium-high until the mixture boils again, then reduce the heat to a simmer. Add the sliced jalapeños and simmer for 5 minutes. The jalapeños will change color and become less bright green.
Fill the jars. Use a funnel to ladle the hot jalapeño mixture into clean, hot half-pint jars, leaving about ¼-inch of headspace. Use a tool to press down the peppers and let any air bubbles escape. Wipe the edges clean so the lids can seal properly. Take the lids and rings from the hot water and screw them on “fingertip tight.” This means tightening until you feel a little resistance but not too much—you should be able to turn it on or off with just your fingertips.
Process. Lower the jars into the boiling water bath canner, cover the pot with the lid, and process for 10 minutes for half-pints or 15 minutes for pints.
Cool and store. Remove the jars from the canner and place them on a clean dish towel to cool at room temperature. Once the lids have been sealed (you should hear a popping sound), let them sit for 24 hours undisturbed. Store the jars in a dark, cool place for up to 1 year.