Preheat your grill to 400°F (204°C).
In a small bowl, mix paprika, garlic powder, cumin, and kosher salt.
Drizzle olive oil over the chicken thighs and season both sides generously with the spice mixture.
Grill the chicken over direct heat with the lid closed, turning once or twice until fully cooked and the juices run clear (about 12–16 minutes depending on thickness).
Remove the chicken and let it rest for several minutes before shredding with two forks.
Meanwhile, heat olive oil in a medium saucepan over medium heat.
Add diced onion and cook until soft and translucent.
Stir in chili powder, garlic powder, and cayenne pepper.
Pour in the root beer and stir well.
Add ketchup, lemon juice, and molasses, then stir until smooth.
Bring the sauce to a gentle boil, reduce the heat, and simmer for about 15 minutes until thickened.
Add the shredded chicken to the sauce and stir until every piece is well coated. This BBQ Pulled Chicken Recipe develops even more flavor after a few minutes of simmering together.
Toast the buns if desired and fill each with the shredded BBQ chicken. Top with coleslaw and serve warm.