Add 1 teaspoon of olive oil to a large saute pan along with the sliced zucchini and clove of garlic. Now, saute the zucchini over medium heat for about 3 minutes or just until it’s slightly soft but still crunchy. Then remove the garlic clove, season the zucchini with a bit of salt and pepper, and set the pan aside for now.
Bring a large pot of salted water to a boil. Then add the spaghetti and cook it according to the package instructions until al dente. When done, reserve 1 cup of the pasta cooking water.
Set aside about 1 tablespoon of the grated cheese. Then whisk the egg yolks, black pepper, and the rest of the cheese together in a small bowl. Now, whisk 1 tablespoon of the pasta cooking water into the egg yolk mixture until it’s creamy.
Add the cooked pasta to the pan with the zucchini. Then add 2 to 3 tablespoons of the reserved pasta water and saute everything together for 1 minute over high heat.
Remove the pan from the heat and turn off the stove. Now, pour the egg yolk mixture over the spaghetti while stirring for about 30 seconds. Then mix in the remaining 1 tablespoon of grated cheese along with 1 to 2 more tablespoons of the pasta water to make the dish nice and creamy.
Finally, serve your vegetarian carbonara with some more freshly ground black pepper and grated Romano cheese if you like!