Make Sauce: In a large Dutch oven or pot, whisk ketchup, vinegar, brown sugar, smoked paprika, cumin, salt, and pepper until smooth.
Cook Chicken: Add chicken to sauce; toss to coat. Bring to a simmer over medium heat.
Simmer: Reduce heat to medium low. Partially cover pot (lid ajar 1 inch). Simmer for 20 mins.
Shred: Uncover. Chicken should be very tender. Shred directly in pot using two forks.
Finish: Increase heat to medium high. Cook, stirring, 5-10 mins until sauce is thickened and clings to chicken.
Serve: Season to taste. Serve on buns, in tacos, salads, etc.