Heat the olive oil and butter in a large skillet over medium heat. Once the butter has melted, add the diced onion and chopped garlic and sauté until the onion begins to soften.
Reduce the heat to low and add the sliced cabbage. Season with salt and pepper. Slowly sauté the cabbage for about 25 minutes, stirring occasionally, until it is very soft and wilted down.
Meanwhile, boil the egg noodles according to the package directions. Before draining them, reserve some of the pasta water. Add the miso paste to a small bowl along with some of the reserved pasta water and whisk until the miso is completely dissolved.
Add the cooked egg noodles to the skillet with the cabbage and pour the miso mixture over everything.
Add the remaining butter and a generous amount of freshly grated Parmesan cheese. Season with additional salt, pepper, and garlic powder to taste, then toss everything together until the noodles and cabbage are evenly coated. Serve warm with additional Parmesan cheese on top, if desired.