Melt the butter in a large pot or Dutch oven over medium heat. Add the carrots, celery and onion and sauté until the vegetables start to turn translucent, about 2 minutes. Add the thyme sprigs, then sprinkle the flour evenly over the vegetables and stir to combine. Next, add the chicken broth, cream, bouillon cube, turmeric and salt and pepper to taste. Bring to the boil, stirring constantly, then reduce the heat to low. Simmer, stirring, until the liquid has thickened and the vegetables are tender, 10 to 12 minutes.
Toast the brioche.
Add the chicken to the pot and stir it into the sauce. Cook for a minute or two, then add the peas and cook for 1 minute more, stirring so that everything is combined.
Place 1 slice of toast on a plate. Top with a ladle of the chicken mixture. Garnish with chives.