Step 1: Wash and slice jalapeños. Wear gloves to protect your hands. Slice off the stem ends and then slice the jalapeños into uniform 1/8 to 1/4 inch rounds. You can remove some seeds and membranes for less heat, if desired.
Step 2: Place sliced jalapeños in a large, non-reactive bowl and set aside.
Step 3: In a large, heavy-bottomed pot or Dutch oven, combine apple cider vinegar, granulated sugar, garlic granules, turmeric, and cayenne pepper (if using). Stir well.
Step 4: Bring the mixture to a rolling boil over medium-high heat, stirring occasionally until the sugar is fully dissolved. Reduce heat to medium-low and simmer for 5 minutes.
Step 5: Carefully add the sliced jalapeños to the simmering syrup. Increase heat slightly to bring back to a gentle simmer. Cook for 10-15 minutes, stirring occasionally, until jalapeños soften slightly and deepen in color.
Step 6: Using a slotted spoon, carefully transfer the cooked jalapeños to clean, sterilized canning jars. Pack them relatively tightly, leaving about 1/2-inch headspace.
Step 7: Return the pot with the remaining syrup to medium-high heat. Bring to a vigorous boil and boil for 5-7 minutes, or until the syrup has thickened to your desired consistency (it should coat a spoon).
Step 8: Carefully pour the hot, thickened syrup over the jalapeños in the jars, ensuring they are completely submerged and you still have 1/2-inch headspace. Tap jars gently to release air bubbles. Wipe rims clean, then apply lids and bands, tightening to fingertip-tight.
Step 9: For shelf-stable storage, process the jars in a boiling water bath for 10 minutes. If not canning, let jars cool to room temperature, then store in the refrigerator. Allow at least 2 weeks for flavors to meld before enjoying.