Heat olive oil in a large pot or Dutch oven over medium heat. Add chicken breasts and cook until browned on all sides. Remove chicken from pot and set aside.
Add onion and mushrooms to the pot and cook until softened, about 5-7 minutes.
Add garlic, basil, oregano, salt, and pepper to the pot and cook for 1 minute more.
Stir in flour and cook for 1 minute.
Gradually whisk in chicken broth until smooth.
Bring to a boil, then reduce heat and simmer for 5 minutes.
Add egg noodles and cook according to package directions.
Return chicken to the pot and cook until heated through.
Stir in frozen peas and cook until heated through.
Serve immediately.