TO PREPARE THE DRESSING: Combine mustard and the egg in a large mixing bowl, mix well and set aside. Place the cream and dried tarragon leaves in a small saucepan and bring to a boil over medium heat on the stove. Remove from heat and whisk hot cream into the mustard-yolk mixture. If using fresh tarragon, add it now. Slowly whisk in 3 tablespoons olive oil. Set the dressing aside.
TO PREPARE THE POTATO SALAD: Cut unpeeled potatoes into 1-inch pieces. Place in a pot, cover with water and place over high heat on the stove and cook until potatoes are soft. Drain potatoes, place in a mixing bowl, pour over the vinegar, cover and let sit for 5 minutes.
TO PREPARE THE CHICKEN: Heat 2 tablespoons oil in a medium skillet over medium heat, add the chicken, cover and cook, 5 minutes for cooked chicken. Scrape the chicken into the bowl with the dressing, add the potatoes and mix well. To serve, add spinach to the bowl, mix well and mound on plates.