When the water is cooking, you can add the pasta. Cook the pasta al dente (for about 8 minutes) or as described on the product package.
In the meanwhile, you can bake the sundried tomatoes until they are hot. Then turn off the heat.
Personally, I love to whisk the egg yolks before adding them to the pasta. Let me give you 2 methods so you can choose:
1. When the pasta is cooked, add it directly to the pan with sundried tomatoes. Add the cheese, basil, a few tablespoons of cooking water and egg yolks and mix directly. The heat of the pasta will cook the eggs, so make sure to move the pasta around for a few minutes.
2. Add the egg yolks to a heat resistant bowl, and whisk until foamy above the cooking pan. The heat of the steam will partly cook the eggs already. When the eggs are light yellow and foamy, and the pasta is cooked, it is time to assemble the dish. Add the cooked pasta to the baking pan with sundried tomatoes. Then add the cheese, basil leaves, a few tablespoons of cooking water and foamy egg yolks.
Serve the pasta directly (with extra cheese!) Enjoy!