Wash the 12 pickling cucumbers well, then cut them into 1/4-inch slices or spears and set them aside while you prep the aromatics and jars. The cucumbers should look fresh and firm, and uniform pieces pickle more evenly.
Smash the garlic cloves, pull the dill away from any thick stems, and sanitize the Mason jars before filling them. Having everything ready makes packing easier and helps keep the dill and garlic evenly distributed.
Combine 4 cups water, 2 cups white vinegar, 2 tablespoons kosher salt, and 1 teaspoon sugar in a medium saucepan and bring the mixture to a boil. When the brine is ready, it will smell bright and sharp with a fresh vinegary aroma, and the salt and sugar should be fully dissolved.
Take the saucepan off the heat and let the brine cool to room temperature before using it for refrigerator pickles. This helps protect the cucumbers from softening and keeps their texture snappy.
Layer the cucumbers, 1 bunch fresh dill, 1 head garlic, skins removed, cloves smashed, and 1 tablespoon peppercorn kernels into the jars without pressing everything in too tightly. Leave a little space between pieces so the brine can move around and season the cucumbers evenly.
Pour in enough cooled brine to fully cover the cucumbers, seal the jars with airtight lids, and refrigerate them. The pickles can be tasted sooner, but the flavor is best after about 1 week when the dill, garlic, and peppercorns have had time to settle in.