Prep the chicken and eggs: Chop the cooked chicken into small, even pieces. Peel and chop the hard-boiled eggs into small chunks.
Build the flavor base: In a medium bowl, combine mayonnaise, Dijon mustard, yellow mustard, lemon juice, garlic powder, paprika, salt, and black pepper. Stir together until well mixed.
Combine ingredients: Add the chopped chicken, eggs, celery, red onion, and chives or parsley to the bowl. Gently mix until everything is evenly coated and combined.
Adjust seasoning: Taste the mixture and adjust salt, pepper, or other seasonings as needed.
Chill (optional): For best flavor, let the mixture chill in the refrigerator for a short time to allow flavors to meld.
Assemble sandwiches: Spread the chicken egg salad mixture onto slices of bread, adding lettuce and tomato if desired. Serve with pickles on the side if using.