One 3-to-4-pound chicken
Kosher salt and freshly ground black pepper
1 large egg (see note)
2 teaspoons Dijon mustard
1 teaspoon vinegar, preferably white balsamic vinegar
¼ cup fresh tarragon leaves
½ teaspoon kosher salt
Freshly ground black pepper, to taste
1 cup neutral oil (such as vegetable oil)
Lemon juice, as needed (optional)
1 small red onion, thinly sliced
1 tablespoon white balsamic vinegar
8 slices of bread, such as Soft Sandwich Bread, sliced ½ inch thick
Arugula or other greens
1. Cook the Chicken: In a large pot, add the chicken and cover it with cold water until completely submerged. Bring to a boil uncovered over high heat, then turn off the heat, cover the pot and let it sit for 1 hour. Remove the chicken from the pot and pull the meat from the bones; some chicken will cling to the bones. (To make stock, do not discard the bones, fat or poaching water.)
2. Make the Tarragon Mayonnaise: Meanwhile, in the bowl of a food processor, combine the egg, mustard, vinegar, tarragon, salt and pepper and purée until smooth. With the motor running, add the oil in a slow, steady stream. Scrape down the sides of the bowl. The mixture will be thick and pale green. Taste and adjust the seasoning as needed.
3. Cut the pulled chicken into bite-sized pieces, then place it in a large bowl. Season with ½ teaspoon kosher salt and pepper to taste. Toss with tarragon mayonnaise to taste. Taste and adjust the seasoning with more salt and pepper as needed. Add lemon juice to taste, if using. Chill until ready to assemble the sandwiches.
4. Make the Quick-Pickled Onions: In a small bowl, combine the onion with a pinch of salt. Cover with the vinegar, and let it sit for at least 10 minutes at room temperature or up to a day in the refrigerator.
5. Assemble the Sandwiches: Top 4 slices of bread with chicken salad, pickled onions and arugula, then top each with the remaining slices of bread.
Note: If using raw egg for the mayonnaise worries you, you can boil the egg for 4 minutes before cracking it into the food processor.