Preheat grill. Smother half of the ⅓ cup bbq sauce on both sides of the chicken breasts, being careful not to contaminate the extra sauce with raw chicken, and cook on medium heat for 4 to 5 minutes per side depending on how thick the chicken is. Make sure the centers reach 165 degrees Fahrenheit. Dice the grilled chicken and toss it in the remaining bbq sauce. Set aside.

Combine both cheeses in a bowl, and gather the remaining ingredients next to the grill for quesadilla assembly.

Lower heat on grill to low. Butter both sides of each tortilla and grill a couple at a time, just until lightly toasted on each side.

Add cheese, diced bbq chicken, diced pineapple, and sliced green onions. Top with another toasted tortilla and grill until golden brown on both sides and cheese is melted, using a spatula/turner to flip the quesadillas.

For the dipping sauce, combine the ranch and bbq sauce and whisk until combined. Serve quesadillas warm with the sauce on the side.