Bring a large pot of water to a boil over high heat. Once boiling, salt the water. Add the pasta and cook until just shy of al dente, according to package directions.
Heads up: you need to reserve about 1 cup of the starchy cooking water just before draining.
While the pasta is cooking, put a large skillet over medium-high heat and add the extra-virgin olive oil. Add the anchovies and cook until they've melted into the oil, about 2 minutes. Reduce the heat to medium-low and add the garlic, stir 1 minute then add in Worcestershire. Shred the escarole and add several handfuls at a time, wilting the greens in the garlic oil. Dress the greens with lots of pepper and a little nutmeg, then squeeze the juice of 1 lemon over the pan. Add the reserved starchy cooking water to the eggs in a small bowl and beat together to temper them. Turn off the heat and add the drained pasta and the egg mixture. Stir to combine. Add half of the cheese and toss vigorously for 1 minute. Dress the pasta with a drizzle of extra-virgin olive oil and transfer to a serving dish. Pass the remaining cheese at the table.