In a bowl, toss the shredded cooked chicken with barbecue sauce, mixing until well coated. Set aside.
In a large skillet or saucepan over medium heat, melt the cream cheese and stir in the milk until smooth.
Add the shredded cheddar and Monterey Jack cheese, stirring continuously until fully melted and creamy.
Stir in the sour cream, smoked paprika, garlic powder, black pepper, and diced jalapeños (if using).
Mix in the BBQ chicken, ensuring it's evenly distributed throughout the dip.
If you want a baked, bubbly top, transfer the dip to an oven-safe dish, sprinkle with extra cheese, and broil at 400°F (200°C) for 5 minutes until golden brown.
Remove from heat and top with chopped green onions, cilantro, and an extra drizzle of BBQ sauce.
Serve warm with tortilla chips, crackers, or toasted bread.