Boil pasta in salted water until just before it's ready (still a little chewy). Reserve 1 cup of the water and drain away the rest.

Once the boiled eggs are cool enough to handle, shell and remove the whites (use for another purpose). Using a fine grater, grate all the yolks. Set aside.

In a large skillet heat 6 Tbsp of the butter along with the garlic, stirring until garlic is fragrant. Stir in lemon zest, juice and pepper flakes. Add in pasta and 1/2 cup of the reserved water, cover and simmer until liquid is absorbed and pasta is tender (add more water as needed), about 5 minutes. Add in cheese and remaining 1 Tbsp of butter and stir until smooth. Season to taste with salt and pepper.

Stir in half the grated egg yolks and the chives into the pasta, tossing to combine. Divide the pasta into 4 bowls and sprinkle with the remaining grated yolks.