Add the entire jar of pickled jalapeño slices, including the liquid, to a blender. Blend until completely smooth, scraping down the sides as needed. The mixture should look like a thin, pale green puree with no visible chunks.
In a mixing bowl, combine the mayonnaise, sour cream, paprika, cumin, garlic powder, onion powder, chili powder, cayenne pepper, and salt. Stir until the mixture is completely smooth and evenly seasoned.
Add seven tablespoons of the blended jalapeño puree to the bowl and mix until fully incorporated. Start with seven tablespoons, then taste and add more puree if desired. Adding too much can make the sauce overly vinegary or too spicy, so increase gradually.
Transfer the sauce to an airtight container and refrigerate for at least one hour before using. This resting time allows the flavors to fully develop.
To assemble the quesadilla, lay a flour tortilla flat. Spread an even layer of shredded cheese, diced chicken, and a drizzle of the creamy jalapeño sauce over half of the tortilla, then fold it in half.
Melt a little butter in a skillet over medium heat. Place the folded quesadilla in the pan and cook until golden brown on both sides and the cheese is melted. Slice into triangles and serve with extra sauce for dipping.
Cook it hands-free.
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