Heat olive oil in a large pot over medium heat.
Add diced chicken, season with salt and pepper, and cook until no longer pink, about 5–7 minutes. Remove and set aside.
In the same pot, sauté onion, carrots, and celery for 5 minutes until softened. Add garlic and cook for 1 minute.
Sprinkle flour over veggies and stir for 1–2 minutes to create a roux.
Gradually pour in chicken broth, stirring to avoid lumps. Add almond milk, potato, thyme, rosemary, and bay leaf (if using).
Bring to a simmer, reduce heat to low, cover, and cook for 15–20 minutes until potatoes are tender.
Add cooked chicken and frozen peas. Cook for 3–5 minutes until peas are bright green.
Remove bay leaf, adjust seasoning with salt and pepper, and garnish with parsley.
Serve hot with crusty bread, if desired.