Heat the oil in a large nonstick skillet over medium heat. Add the onion and pepper flakes and sauté until the onion is tender, about 5 minutes. Add the wine and simmer until reduced by half, about 30 seconds. Remove the pan from the heat.

Cook the pasta in a large pot of boiling salted water 8 minutes. Add the greens and cook until the pasta is just tender but still firm to the bite and the greens are tender, about 2 minutes longer.

Meanwhile, break the eggs into a small bowl and beat with a fork to blend. Mix in both cheese and a generous amount of black pepper.

Remove ½ cup of the pasta cooking water and reserve. Drain the pasta and greens.

Reheat the onion mixture briefly and then remove from the heat. Add the spaghetti and greens to the skillet. Gradually whisk ¼ cup of the hot pasta water into the egg mixture. Add the egg mixture to the skillet and toss until it coats the pasta and is creamy, not wet and runny. If the egg mixture does not become creamy, set the pan over very low heat and stir constantly just until it becomes creamy, watching carefully (do not boil). Immediately remove the pan from the heat. Mix in enough of the remaining ¼ cup pasta cooking liquid to form a silky texture, if needed. Season to taste with salt and pepper. Divide the pasta between 2 warmed plates and serve.