Scrub the clams under cold water and soak them in a 25 cm / 10-inch bowl with 1 liter of cold water and 2 tbsp coarse sea salt for 20 minutes. While they soak, scrub the mussels and pull off the beards. Discard any mussel with a cracked shell or one that stays open when tapped. Pat the shrimp dry and grate the Parmigiano.

In a 20 cm / 8-inch bowl, whisk the egg yolks, whole egg, Parmigiano and black pepper until smooth. Set aside. Fill a 6-quart / 5.7 L pot with 4 liters of water, add 2 tsp coarse sea salt and bring to a boil.

Drop the spaghetti into the boiling water and set a timer for 1 minute less than the package time, usually 8 to 9 minutes. Lift the clams out of their soaking water by hand and leave the grit behind.

One minute later, warm the olive oil and garlic in a 30 cm / 12-inch deep sauté pan over medium heat for 1 minute, until the garlic turns pale gold. Pour in the wine and let it bubble for 30 seconds. Add the clams and mussels, cover, and cook over medium-high heat for 5 to 6 minutes, shaking the pan once or twice, until the shells open. Move the opened shellfish to a bowl with tongs and throw out any that stayed shut.

Add the shrimp to the pan liquor and cook for 2 minutes, turning once, until pink and opaque. Move them to the shellfish bowl. Pull the meat from half the mussels and clams while the pasta finishes, and leave the rest in their shells.

Scoop out 250 ml pasta water, then drain the spaghetti and add it to the pan with the shellfish liquor. Toss over low heat for 1 minute, until the strands absorb the liquor and look glossy.

Take the pan off the heat and wait 60 seconds. Pour in the egg mixture plus 60 ml pasta water and toss with tongs for 1 to 2 minutes, until the sauce clings to the strands like loose custard. Add more pasta water 1 tbsp at a time if it looks tight. Fold in the seafood and parsley, divide among warmed bowls and serve within 5 minutes.