Heat olive oil in a large stockpot or Dutch oven over medium heat.
Add chicken to the stockpot and season with salt and pepper. Cook until lightly browned, about 2-3 minutes; set aside.
Melt butter in the stockpot over medium heat. Add mushrooms, onion, carrots and celery and cook, stirring occasionally, until tender, about 3-4 minutes.
Stir in thyme and garlic and cook until fragrant, about 1 minute.
Stir in flour and cook until lightly browned, about 1 minute. Whisk in chicken stock and cook, whisking constantly, until slightly thickened, about 4-5 minutes.
Add bay leaf and chicken thighs, and stir in half and half.
Bring to a simmer and cook until heated through.
Remove bay leaf before serving.
Garnish with parsley and rosemary.