Cook the egg noodles according to the directions on the package.
In a pot, add the broth, onion, carrots, chicken, mushrooms, salt, and thyme and bring to a boil over high heat. Once boiling, turn down to a simmer for 25 minutes.
In a bowl, dissolve the flour in an equal amount of water, whisking to remove all lumps.
Remove the chicken from the pot, using two forks pulling in the opposite direction, shred the chicken and return it to the pot. Add in the peas and cream.
Make sure the pot is simmering, slowly stir in the flour/water mixture. Simmer for about 10 minutes until it is nice and thick. Season with salt and pepper to taste.
Remove the thyme sprigs, serve over noodles. Garnish with parsley.