Place turnip slices in a large bowl. Sprinkle with kosher salt and massage gently until they release some liquid.
Let sit for 1–2 hours, then rinse thoroughly and drain.
In a small bowl, mix gochujang with water to create a spreadable consistency.
Stir in the garlic, ginger, scallions, fish sauce, and cayenne (if using).
Toss the turnips with the kimchi paste until evenly coated.
Pack the turnip mixture tightly into a clean jar, pressing down to remove air pockets and ensuring the turnips are submerged in the paste.
Leave about 1 inch of headspace in the jar. Loosely cover with a lid or cheesecloth to allow gases to escape during fermentation.
Store at room temperature (65°–75°F) for 3–5 days. Taste daily until it reaches your preferred tanginess.
Once fermented to your liking, seal tightly and refrigerate. Use within 1 month.