Dredge chicken thighs in flour.
Save any unused flour and add additional flour to make about 1/3 cup; set aside.
Heat beef tallow in a large, 14-inch skillet over medium heat.
Brown chicken thighs well on both sides.
(Because the pan is so large, you may need to turn it about so all the pieces get well-browned.)
Sprinkle chicken evenly with half of the thyme, half of the salt, half of the parsley and all of the ground black pepper.
Add chicken broth around the outside edges of the skillet.
(Try not to pour the chicken broth over the meat or it will wash off all of the seasonings.)
Cook chicken, covered with lid, about 10-15 minutes over medium heat.
Meanwhile, wash gold potatoes and peel.
If the potatoes are really large, halve the potatoes.
Add potatoes to skillet along with baby carrots and onion.
Sprinkle vegetables with remaining thyme, parsley and salt.
Bring to a boil.
Reduce heat and cover with lid.
Cook chicken and vegetables over low to medium heat about 45-60 minutes, or until chicken thighs and vegetables are tender.
(If you feel that most of the broth has cooked down after 30 minutes, add an additional cup of chicken broth.
Add carefully pouring in the crevices so the thyme and parsley are not washed off the vegetables.)
Use leftover flour by spooning into a measuring cup.
Add enough water to make a thin paste.
Keep stirring with a fork or small whisk until the flour is completely dissolved and no lumps remain.
If you have not added the fourth cup of chicken broth yet, and if the chicken broth has cooked down too much, add an additional cup of chicken broth now.
Slowly add flour mixture and stir into skillet crevices (between pieces of chicken and vegetables) and stir gently and carefully into the broth.
Cover with lid and allow the gravy to thicken by cooking an additional 5-10 minutes.
Sprinkle meat and vegetables with additional thyme, if desired, and dried or fresh, minced parsley.
Serve.