METHOD
Make Aïoli: place egg yolks, garlic, mustard, lemon juice and salt in a food processor and blend to combine. With the motor running, very slowly drizzle in the oil to make a smooth, thick sauce. Place in a serving bowl and set aside.
Bring a large saucepan of salted water to the boil. Add periwinkles, return to the boil, reduce heat and simmer for 5-10 minutes, depending on size.
Strain and arrange on a platter with aïoli on the side and a bamboo or metal pick for pulling the periwinkles from their shells.