Put the chicken and the bay leaf in a small pan and add water, almost to cover the chicken. Bring to a boil over high heat, then reduce the heat and poach the chicken until cooked through, about 10 minutes. Remove the chicken to a plate. Strain the broth and reserve
Meanwhile, heat the extra-virgin olive oil, a turn of the pan, in a soup pot or Dutch oven over medium-high heat. Add the carrots, celery, onions, garlic, potatoes, salt and pepper, to taste. Stir, cover, and cook 7 to 8 minutes, stirring occasionally to sweat the veggies. Add the stock and bring to a boil, then simmer to keep the stock at a low boil. Dice the poached chicken then stir it into the stock. Add the peas, tarragon, thyme, and parsley.
In a small pan over medium heat, melt the butter and whisk in the flour. Cook for 1 minute, then stir it into the soup to thicken. Add the reserved strained chicken poaching liquid to loosen up the sauce remember that youre going for a consistency thats thicker than soup and thinner than stew. Season with salt and pepper, to taste. Transfer to a serving bowl and serve.