Combine the wine with about 3 quarts salted water and bring to a boil. Add the pasta and cook until al dente. Drain, reserving 1 cup of the pasta cooking water.
Meanwhile, in a large skillet, heat the EVOO, 4 generous turns of the pan, over medium-high heat. Add the portobellos and brown for about 10 minutes. Add the garlic and stir for 1 minute. Add the kale and wilt; season with salt, pepper and nutmeg to taste. Cover the pan and lower the heat to medium-low, stirring occasionally, for 10 minutes. Toss the pasta with the kale and enough pasta cooking water to combine; adjust the seasonings and top the pasta liberally with the pecorino-romano.