Make the jalapeño cream sauce: blend jalapeños, sour cream, cream cheese, garlic, lime juice, and cilantro until smooth. Thin with water if needed. Season with salt and refrigerate.
Make the hot honey: combine honey, hot sauce, red pepper flakes, and garlic powder in a small bowl. Heat gently for 30 seconds and stir until combined.
Coat the chicken: toss shredded chicken with two-thirds of the hot honey. Season with salt and pepper. Reserve remaining honey for drizzling.
Cook quesadillas: heat oil or butter in a large skillet over medium heat. Place a tortilla flat, scatter cheese over the whole surface, add hot honey chicken to one half, fold over. Cook 2 to 3 minutes per side until golden and crispy and cheese is fully melted. Repeat for all four.
Rest and slice: let quesadillas rest on a cutting board for 1 minute before slicing into 3 wedges each. Drizzle reserved hot honey over the top.
Serve immediately with jalapeño cream sauce on the side for dipping.