In a large pot, such as a dutch oven, heat olive oil over medium heat. Add the sliced shallot and stir while cooking until they soften, about 2 minutes. On top of the shallots, add the sliced cabbage along with 1/2 tbsp kosher salt. Gently stir and allow the cabbage to steam and cook down.
Once the cabbage volume has reduced by about half, add the garlic powder and a few good cracks of black pepper. Stir and continue to cook over medium heat. The cabbage will continue to reduce.
When the cabbage has shrunk to a point where you can easily see parts of the bottom of your pot, add the white wine. Raise the heat slightly and stir until the wine cooks off. Lower heat to low. Add the white miso paste and stir until it is fully combined with the cabbage (you may want to add more water to help the miso combine).
Remove the pot from the heat. Add the cooked pasta along with the salted butter and approximately 1/4 cup of the pasta water. Grate on the parmesan cheese and allow it to sit for 1 minute to begin melting. Add another splash of pasta water on top of the cheese, then stir heavily to combine until the cheese and butter are fully melted. Taste and add more salt and pepper as desired. Add more pasta water as needed and discard what is unused.
Once the cabbage forms into a sauce with pasta water and cheese, serve the pasta hot on a plate, scooping more cabbage on top of the plated pasta. Garnish with more grated parmesan, black pepper, a squeeze of lemon, and finely chopped parsley.