Place turkey wings and onions in a greased 13x9-in. baking pan. Bake, uncovered, at 400° for 1-1/4 hours, turning once.
Transfer wings and onions to a Dutch oven. While 13x9-in. pan is still warm, carefully add 2 cups broth. Using a spatula, gently scrape any brown bits off bottom of pan; pour into Dutch oven with wings. Add 4 cups broth, carrots, celery and thyme to Dutch oven. Bring to a boil. Reduce heat; simmer, uncovered, about 45 minutes.
Strain; discard wings and vegetables. (Can be made ahead to this point and stored in the refrigerator for up to 2 days.) Skim fat from cooking liquid. Add enough remaining broth to measure 3-1/2 cups.
In a large saucepan, whisk flour and 3/4 cup remaining broth until smooth (if any broth remains, save for another use). Gradually stir in cooking liquid. Bring to a boil; cook and stir until thickened, about 2 minutes. Stir in butter and pepper.