1. Heat 2 tablespoons of olive oil in a large, deep-sided skillet over medium-high heat.
2. Add the chorizo, ensuring it’s all in an even layer. Let the sausage get really browned and crusty before turning or stirring it. Cook the chorizo through (takes about 5 minutes total) and, using a slotted spoon or fish spatula, transfer to a paper towel-lined plate. Leave the drippings in the pan. Lower the heat to medium and add the cabbage and the chili (if using). You can add a little olive oil, if needed.
3. Cook, stirring occasionally, until wilted and very tender; about 10 minutes. Season lightly with salt and pepper.
4. Meanwhile, bring a large pot of salted water to a boil. Cook the pasta until al dente, about 2 minutes less than the package instructions. When it’s done, reserve 1 cup of the starchy cooking water.
5. Transfer the pasta to the pan with the spicy cabbage.
6. In a bowl, whisk together the egg yolks, egg, about half of the pecorino, ½ teaspoon salt, and lots of freshly cracked black pepper.
7. Add ½ cup of the warm, starchy pasta water, whisking as you do. With the heat off under the pasta, add the egg sauce and toss enthusiastically to get everything nice and coated. When it’s all steaming and hot, the sauce should be thickened and where you want it to be. You can add a little more pasta water to loosen and thin out the sauce, if needed.
8. Add the chorizo to the pasta and toss.
9. Serve the pasta with more pecorino on top, and some extra pepper and a drizzle of olive oil to finish, if desired

Recipe Notes: To lighten further, substitute a chicken sausage and only use 1/2 pound of pasta.