In a Dutch oven or similar large, deep pot, heat the oil over medium-high heat. Add the onion and cook until softened and browned at the edges, about 10 minutes.
To the pot, add the cabbage, 1/2 teaspoon kosher salt, and 1/4 cup water. Cook, stirring occasionally, until the cabbage is tender, about 10 to 15 minutes. Every few minutes, run a wooden spoon along the bottom of the pot to make sure the cabbage and onions aren't sticking. If they are splash in a few tablespoons of additional water to loosen them (repeat adding water as often as necessary).
Meanwhile, bring a large pot of well-salted water to a boil. Add the noodles and cook until al dente (about 7 minutes, or according to package instructions). Drain.
Once the cabbage is softened, stir in the smoked paprika, black pepper, soy sauce, and remaining 1/2 teaspoon salt. Cook until fragrant, about 30 seconds.
Turn off the heat. Add the drained noodles and butter. Stir so the butter melts and everything is nicely combined.
Stir in 1 teaspoon of the vinegar or lemon juice. Taste and add more salt and pepper as desired. Serve warm.
Notes
TO STORE: Store leftover cabbage and noodles in an airtight container for up to 4 days.
TO REHEAT: Warm gently in a skillet with a splash of water or broth and a small pat of butter.