Preheat the grill to 400°F (204°C).
In a small bowl, combine the paprika, garlic powder, cumin, and kosher salt.
Drizzle the chicken thighs with 1 tablespoon of olive oil, then generously season both sides with the spice mixture.
Place the seasoned chicken on the preheated grill over direct heat. Close the lid and grill, turning once or twice, until the chicken is nicely browned and reaches a safe internal temperature of 165°F (74°C).
Transfer the grilled chicken to a clean plate and allow it to rest for several minutes.
While the chicken rests, prepare the BBQ sauce. Heat 1 tablespoon olive oil in a medium saucepan over medium heat.
Add the diced onion and cook, stirring frequently, until soft and translucent.
Stir in the chili powder, garlic powder, and optional cayenne pepper. Cook briefly until fragrant.
Pour in the non-alcoholic root beer and stir well.
Add the ketchup, fresh lemon juice, and molasses. Stir until completely combined.
Bring the sauce to a gentle boil over medium-high heat. Reduce the heat to medium-low and simmer for approximately 15 minutes, stirring occasionally, until thickened.
Using two forks, shred the rested chicken into bite-sized pieces.
Add the shredded chicken directly to the homemade BBQ sauce and stir until every piece is generously coated.
Toast the buns if desired, then pile the BBQ Pulled Chicken onto each bun.
Top with crunchy coleslaw and serve warm.