These are actually easier to slice if rolled a few hours ahead and left to set in the refrigerator.
Slice cold, and let return to room temperature before serving. They’re perfect for cocktail parties or a buffet brunch; stick a toothpick in each roll, and pass them around.
For the pesto, in a mini–food processor combine the basil, parsley, olive oil, and salt, and process to make a smooth paste. Scrape into a small bowl, and stir in the mayonnaise. Refrigerate while you make the frittate.
For the frittate, in a large bowl, whisk the eggs, milk, scallions, thyme, and salt until smooth.
Heat a large (12-inch) nonstick skillet over medium heat, and add 1 tablespoon of the olive oil. When the oil is hot, add half of the egg mixture, and quickly swirl the pan to make an even layer. Cook until the bottom is set, about 1 to 2 minutes, then flip (using a wide spatula if it needs coaxing). Cook until the underside is light golden and the frittata is cooked through, 1 to 2 minutes more. Remove to a plate. Repeat with the remaining oil and egg mixture. Let the frittate cool.
To assemble, spread half of the pesto on each frittata, spreading it almost all the way to the edges. Roll each frittata into a tight cylinder. Cut each rolled frittata into ten pieces.
Excerpt from "Lidia's Celebrate Like An Italian" by Lidia Matticchio Bastianich and Tanya Bastianich Manuali. Copyright © 2017 by Lidia Matticchio Bastianich and Tanya Bastianich Manuali. Used with permission by Knopf. All rights reserved.