Bring a large pot of salted water to a boil.

Add spaghetti and cook until al dente. Reserve 1/2 cup of cooking water before draining.

While the pasta is cooking, thinly slice the garlic cloves.

Drain the anchovies from their oil and chop them.

In a large skillet, heat olive oil over medium heat.

Add the sliced garlic and anchovies to the skillet and cook until the anchovies dissolve and the garlic is fragrant, about 5 minutes.

Add the oregano, parsley and red pepper flakes to the skillet.

Add the drained spaghetti to the skillet with the anchovy mixture.

Toss the spaghetti to coat it well with the oil and spices.

In a small bowl, whisk together the egg yolks and the reserved pasta water.

Pour the egg yolk mixture over the spaghetti in the skillet.

Cook over low heat, tossing continuously until the sauce becomes creamy and coats the pasta evenly. This should take about 2-3 minutes.

Season with salt and pepper to taste. Be careful with salt, as the anchovies are already salty.

Serve immediately, garnished with extra parsley if desired.