Pour ½ cup of the chicken broth into a measuring cup and set aside.
In a 10-inch cast iron or deep-sided skillet, melt the butter over medium-high heat. Add the onion, celery and carrots. Season with salt and pepper. Cook, stirring occasionally, until the vegetables are tender, about 5-6 minutes.
Add the garlic, thyme and bay leaf. Cook, stirring, until fragrant, about 30 seconds.
Pour in 3 cups of the chicken broth and bring it to a simmer. Whisk the reserved ½ cup of broth with the cornstarch to make a slurry. Slowly pour the slurry into the simmering broth while whisking. Bring to a boil, then reduce the heat to a simmer and cook 5 minutes, stirring occasionally.
Whisk in the crème fraiche. Add the chicken and peas, and season to taste with salt and pepper. Discard the bay leaf. Let cool for at least 30 minutes. Do Ahead: The chicken stew can sit at room temperature for up to 2 hours, or it can be refrigerated for up to 1 day.