Bring a large pot of water to a boil, salt it, add the pasta and cook until al dente. Drain, reserving a cup of the pasta cooking water.
While the pasta is working, heat the EVOO, 4 turns of the pan, in a large skillet over medium heat. Add the anchovies, cover the pan with a splatter screen or loose foil and let the anchovies melt into the oil. Add the chile pepper and garlic and stir for 2 minutes. Add the kale and let it wilt; season with a little nutmeg.
In a measuring cup, beat the egg yolks with some of the reserved pasta cooking water. Toss the drained spaghetti with the kale, a few handfuls of pecorino-romano, lots of black pepper and the tempered egg yolks; add more pasta cooking water as necessary to evenly coat. Serve the pasta in shallow bowls.