Clean vegetables to wash dirt off. Remove any dark green tough outer leaves from cabbage and compost or use for another purpose.
Slice a cabbage head in half lengthwise, so that stem keeps each half together. Shred each half into ¼” ribbons using v-slicer, mandoline, or chef’s knife.
Add shredded cabbage to a large mixing bowl. Brine will form as salt draws water from cabbage.
Sprinkle salt over cabbage.
Finely dice or run garlic cloves over a microplane. Add to bowl.
Finely chop dill sprigs. Add to bowl.
Squeeze or pound the mixture with your clean hands or a kraut pounder for about 5 minutes to break more cell walls and encourage more water to come out of vegetables.
Cut cucumber(s) into quarters lengthwise, then into 1/2" (1cm) chunks. Add last after you've mashed up the cabbage (so you don't mash up the delicate cukes).
Add mixture to a glass jar(s) or a ceramic crock (food-grade plastic containers are also acceptable.) Make sure to get every last drop of brine that has formed in bowl!
Pack down contents so that surface is even and flat.