Melt butter in a large skillet over medium-high heat.  Cook onion, celery and thyme until onion is very soft and golden brown, about 5 minutes.  Stir in flour and cook, stirring constantly, about 4 to 5 minutes or just until light golden brown.

Gradually whisk in 2 cups broth.  Cook, stirring frequently with a whisk, about 3 minutes or until thickened and smooth.  Let cool.  Refrigerate gravy base and remaining 2 cups broth up to 2 days before serving.

Transfer roasted turkey to a platter to rest. Skim fat from pan drippings.  Add pan drippings to refrigerated gravy base in a medium saucepan; heat over medium heat, stirring frequently with a whisk.  Add reserved broth 1/4 cup at a time until desired consistency is reached.  Simmer until heated through and season to taste with pepper.