Add the chopped mushrooms to a saucepan with 1 teaspoon of salt and the bay leaves. Bring to a boil and cook for about 5 minutes, just until tender. Drain well, discard the bay leaves, and let the mushrooms cool completely.
While the mushrooms cool, peel the celery root and grate it using a box grater. Place the grated celery root into a large mixing bowl.
Chop the ham into small, bite-sized pieces and add it to the bowl with the grated celery root.
Season the chicken thighs with salt and black pepper and let them rest for about 5 minutes. Heat a skillet over medium heat and sear the chicken until golden and fully cooked, about 8–10 minutes per side. Let cool slightly, then chop into pieces.
Add the chopped chicken, cooled mushrooms, and freshly chopped parsley to the bowl with the other ingredients.
Stir in the mayonnaise and Dijon mustard, if using. Season with additional salt and black pepper to taste, then gently toss until everything is evenly coated.
Cover the salad and refrigerate for at least 2 hours before serving. This resting time allows the flavors to fully come together.