Remove any tough outer leaves from the red cabbage. Cut the cabbage into quarters, remove the core, then slice very thinly (about 1/8 inch / 3 mm). You should have roughly 8–10 cups of shredded cabbage. Place the shredded cabbage in a large bowl.

Salt and wilt

Sprinkle 1 1/2 tablespoons kosher salt and 3 teaspoons sugar over the shredded cabbage. Using clean hands, massage and toss the cabbage for 2–3 minutes until it softens and releases some liquid. Let sit 20 minutes to draw out more moisture, then drain off and reserve any liquid.

Prepare brine

In a small saucepan combine 1 cup apple cider vinegar, 1 cup water, 1 teaspoon black peppercorns, 1 teaspoon whole mustard seeds, 1 bay leaf, and 1 clove smashed garlic. Add the reserved cabbage liquid (if any). Bring to a gentle simmer over medium heat and stir until the sugar dissolves (about 3–4 minutes). Remove from heat and stir in 1 tablespoon olive oil and 1 teaspoon lemon juice if using. Let the brine cool for 5 minutes.

Pack and infuse

Place the drained shredded cabbage and thinly sliced 1/2 red onion into a clean wide-mouthed jar or airtight container, layering in the optional thyme sprigs. Pour the warm brine over the cabbage mixture, pressing the cabbage down so it is fully submerged in liquid. If necessary, weigh the cabbage down with a small plate or a clean jar lid to keep submerged.

Marinate

Let the jar cool to room temperature (about 30 minutes), then seal and refrigerate. Refrigerate at least 6 hours for light flavor, preferably 24 hours for best taste and color; it will continue to mellow and develop for up to 2 weeks. Keep refrigerated; will keep 2–3 weeks.

To Serve

Before serving, drain excess brine if desired. Toss pickled cabbage with 1/4 cup toasted walnuts or pumpkin seeds and 1/4 cup crumbled feta or goat cheese for texture and richness. Serve chilled or at cool room temperature as a side, on sandwiches, tacos, grain bowls, or salads.