Special equipment: Canner
Prepare the jars and lids:
Wash all jars and lids thoroughly with soap and water and rinse well. Fill your canner with enough water to cover the jars by at least 1 inch and bring to a simmer. Using a pair of canning tongs, lower the jars in gently, tilting them to fill with the hot water. In a small saucepan, keep some water warm but not boiling; place the lids in the water. Have an additional kettle of water on to boil.
Prepare the brine.
Add vinegar, water, salt and garlic and peppercorns or honey (if using), to a medium saucepan and place over medium heat. Bring to a boil, and reduce heat to keep at a simmer.
Prepare the jalapenos.
Wearing latex or plastic gloves, slice the jalapenos into 1/4-inch rings. Add the rings to the brine and bring back to the boil.
Fill and close the jars.
Using canning tongs, remove the jars from the canner, carefully pouring the water back into the canner. Set next to the jalapenos in the saucepan. Turn the heat under the canner to high. Use a ladle to pour the jalapenos into the jars through a canning funnel, leaving 1/2 inch of headspace at the top. Run a clean chopstick around the inside of the jar to dislodge any trapped air. Wipe the rims of the jars with a damp paper towel. Place the lids on, and screw on the rings until just finger-tight.
Seal the jars.
Using canning tongs, gently transfer the jars to the canner, taking care to keep them vertical. When all the jars are in the canner, there should be at least 1 inch of water covering them; if you need more, add water from the kettle until the jars are sufficiently covered. Bring the water to a full rolling boil, and process for 5 minutes.
Remove and cool.
Using canning tongs, gently remove the jars from the canner and transfer them to a kitchen towel or cooling rack, again keeping them vertical. Do not set hot jars directly onto cool counter surfaces. Leave to cool, undisturbed, for at least 12 hours. If any of the jars do not seal when cool, reprocess using the method above, or refrigerate and use immediately.
Label and store.
Add a label to the lid or side of your jar, noting the date it was canned. Remove the rings and store jars in a cool, dark place for up to one year. Refrigerate after opening. Properly-handled sterilized equipment will keep canned foods in good condition for years. Sterilizing jars is the first step of preserving foods.