Make the sauce: To a food processor, blender or a wide mouth mason jar, add cottage cheese, chives, lemon juice, shallots, apple cider vinegar, garlic, and salt, and blend on high until thoroughly combined. Add 2 tablespoons of water to loosen and blend. Set aside.
Make the chicken salad: Remove the skin from the chicken breasts and use your hands to meticulously pull the meat off the bones, discarding the imperfections like soft tendons, cartilage, and red pieces. Measure out 3 cups of chicken and reserve the rest for a different recipe.
Note: You can save the bones in your freezer to make chicken stock in the future.
Divide the chicken into two groups: perfect, moist pieces in one group and dry, not-so-perfect pieces in another. Coarsely chop the perfect, moist pieces and put them in a large bowl. Put the dry, not-so-perfect pieces in a food processor and pulse for 5 seconds, then transfer to the bowl with the perfect pieces and mix.
Add the onion, celery, all of the cottage cheese sauce, chives, giardiniera, salt, and pepper. With a large spoon or spatula mix well until thoroughly combined. Store in a jar or glass container and store