Melt the butter in a large pot over medium heat. Add the potatoes, carrots, celery and onion. Cook until the onions are tender (about 5 minutes).
Stir in the flour until blended. Then slowly add the chicken broth, salt , pepper, thyme and nutmeg. Bring to a light boil over medium high heat, stirring occasionally. Boil until the potatoes are fork tender.
Reduce the heat to low so it is no longer at a boil. Then add a spoonful or the soup to the half and half to temper it. Stir together and then slow stir into the soup. Add the chicken and frozen peas. Heat through and then add more salt, pepper and thyme if desired.