Bring a large pot of salted water to a boil. Add the egg noodles and cook until al dente. Drain and set aside.
Heat 1 tablespoon (15 g) butter in a large skillet over medium heat until melted and starting to sizzle. Add the sliced mushrooms, season with a generous pinch each of salt and pepper and cook, stirring occasionally, until mushrooms are seared and cooked through, about 6–8 minutes. Add the garlic and drained chickpeas and stir to combine. Sprinkle the flour over the mushroom and chickpea mixture, and stir a few times until flour is toasted and no longer white. Take care not to mush the beans and mushrooms together.
Add the Marsala wine and water to the pan, using a wooden spoon or silicone spatula to scrape up any browned butter bits. Reduce the heat to medium low and cook, stirring occasionally, until the sauce thickens, about 5–6 minutes. Remove from heat and stir in the remaining 1 tablespoon (15 g) of butter, balsamic vinegar and parsley. Season with salt and pepper to taste, if necessary, and serve over cooked
VEGAN VERSION: Replace butter with non-dairy butter, same amount. Replace egg noodles with egg-less noodles.