Put the chicken and the bay leaf in a small pan and add enough water to 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 EVOO, one turn of the pan, in a soup pot or Dutch oven over medium-high heat. Add the carrots, celery, onion, garlic, potato and salt and pepper, to taste. Stir, cover and cook for 7-8 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 the mixture into the soup to thicken. Add the reserved strained chicken poaching liquid to loosen up the sauce – remember that you’re going for a consistency that’s thicker than soup and thinner than stew. Season with salt and pepper, to taste. Transfer to a serving bowl and serve.