Cut the ends off green beans. Measure them by the jars and cut them to fit in lengthwise, with an inch of headspace at the top.
Place half of one grape leaf or a few mesquite leaves into the bottom of each of 6 quart-size jars. Fill jars with green beans, tightly packing them into the jar.
Use a butter knife to gently slide in 1-2 cayenne peppers per jar. Do the same for the dill sprigs, 1-2 per jar. Add 1-2 teaspoons crushed peppercorns atop the green beans, followed by 2-3 garlic pieces.
Pour 2 tablespoons of apple cider vinegar into each jar, then fill with brine solution, leaving 1 inch headspace at the top.
If necessary, weigh the beans down under the brine.
Cover each jar with a tight lid, airlock lid, or coffee filter secured with a rubber band.
Culture at room temperature (60-70°F is preferred) until desired flavor and texture are achieved. If using tight lids, burp daily to release excess pressure.
Once the beans are finished, put a tight lid on each jar and move to cold storage. The flavor will continue to develop as beans age.