Place wings, onions, carrots, celery, vinegar, salt, peppercorns, thyme, and bay leaves in a large stockpot; add stock. Bring to a boil over medium-high; reduce heat to low, and cook, uncovered, at a bare simmer until wings fall apart, about 2 hours. Strain and discard solids.

Return strained broth to stockpot; simmer over medium-low heat until reduced to 8 cups, about 1 hour. (The broth should be golden brown and taste like turkey soup.) Transfer broth to a large bowl; place bowl on top of a separate large bowl filled with ice. Let stand, stirring occasionally, until broth cools to room temperature, about 30 minutes.

Store broth covered in refrigerator up to 3 days, or divide broth into 2 (1-quart) containers, and freeze up to 3 months.