Don't step away from the stove when making brown butter—it can go from nutty and fragrant to burned in a flash. Slideshow: More Healthy Pasta Recipes
Heat the butter in a small skillet over moderate heat, swirling occasionally, until nutty and very fragrant, about 5 minutes. Remove from the heat. Take care not to let the butter burn. Pour 4 tablespoons of the brown butter into a large skillet. Set aside.
Add the bread crumbs to the remaining butter in the small skillet, and stir to combine. Add the red pepper flakes and season with salt. Heat over moderate heat and toast, stirring occasionally, until the bread crumbs are crisp and golden, 3 to 5 minutes. Remove from the heat and set aside.
Add the cabbage and currants to the large skillet and cook over moderate heat, stirring occasionally, until the cabbage is wilted but still crisp, about 5 minutes. Stir in the vinegar and season with salt and pepper. Keep warm over very low heat.
Meanwhile, cook the spaghetti in a large pot of boiling well-salted water until al dente. Set aside 1 cup of the pasta cooking water, then drain well. Add the pasta to the large skillet and toss to combine, adding some of the pasta cooking water to moisten the pasta as needed. Serve immediately, topped with the toasted bread crumbs.