Shred Oaxaca and Monterey Jack cheese and mix together. Dice rotisserie chicken. Slice onion and peppers. Roast poblano pepper at 400°F for 25 minutes, flipping halfway, then peel, deseed, and dice finely.
Heat a skillet over medium-high. Cook onions and peppers with a little oil until softened and slightly charred. Remove and set aside.
In a small bowl, mix sour cream, diced roasted poblano, lime juice, salt, and cilantro. Stir until combined and refrigerate until ready to use.
Heat skillet or griddle over medium. Place tortilla directly on the hot surface and spread butter on the top side. Flip so buttered side is down. On one half of the tortilla, layer ½ cup chicken, a spoonful of fajita vegetables, and ½ cup of the cheese mixture. Fold tortilla in half and press lightly.
Cook for 2 to 3 minutes until golden and cheese begins to melt. Flip and cook the other side until crisp. Repeat with remaining tortillas.
Cut quesadillas into triangles and serve hot with roasted poblano crema.