Heat olive oil in a large pot over medium heat until shimmering, about 1 minute.
Add onion, garlic, carrots, and celery. Cook for 5-7 minutes, stirring occasionally, until vegetables soften and onion becomes translucent.
Stir in shredded chicken, chicken broth, peas, thyme, and rosemary. Bring to a gentle simmer, about 3-4 minutes.
In a small bowl, whisk together flour and heavy cream until completely smooth with no lumps.
Gradually add cream mixture to pot in a slow stream, stirring constantly to prevent lumps from forming.
Continue simmering for 10-15 minutes, stirring occasionally, until soup thickens to coat the back of a spoon. Season with salt and pepper to taste.
Serve hot, garnished with freshly chopped parsley.
Notes
For lighter option, substitute heavy cream with half-and-half or unsweetened almond milk. Add extra tablespoon of flour if using milk alternatives.
Rotisserie chicken saves time. Use leftover holiday turkey for variation.
To cook raw chicken: Season 1 pound chicken breast with salt and pepper. Bake at 375°F for 25 minutes or poach in simmering water for 15-20 minutes until internal temperature reaches 165°F. Shred when cool.
Soup thickens when refrigerated. Add splash of broth when reheating to thin.