Season the Chicken: Place both chicken breasts on a cutting board and pat them dry with paper towels to remove all surface moisture. Combine 0.75 teaspoon of kosher salt, the black pepper, ground cumin, smoked paprika, and garlic powder in a small bowl and stir until evenly mixed. Sprinkle the spice blend across all surfaces of both breasts, pressing gently so the seasoning adheres. Set the seasoned chicken on a clean plate and let it rest uncovered at room temperature for 15 minutes. This dry-brine period draws moisture to the surface, dissolves the salt, and allows the seasoning to penetrate into the outer layer of the meat.
Cook the Chicken: Heat 1 tablespoon of avocado oil in a 12-inch nonstick skillet over medium-high heat for 2 minutes until the oil shimmers and flows freely when the pan is tilted. Place both chicken breasts smooth-side down in the skillet and cook for 6 minutes without moving them until the undersides are deeply golden brown. Flip each breast with a wide flat spatula and cook for 5 more minutes until an instant-read thermometer inserted at the thickest point reads 74°C / 165°F and the juices run clear. Transfer the chicken to the cutting board and tent loosely with foil.
Rest and Slice the Chicken: Allow the cooked chicken breasts to rest on the cutting board for 5 minutes before slicing. Resting lets the internal juices redistribute throughout the meat rather than spilling out onto the board when cut. After 5 minutes, slice each breast against the grain into strips 0.5cm / 0.2in thick, then cut those strips crosswise into bite-sized pieces approximately 1.5cm / 0.6in long. Uniform pieces distribute evenly across the tortilla and prevent any single bite from being overloaded or sparse.
Saute the Aromatics: Wipe out the skillet with a folded paper towel held with tongs to remove residual oil and fond without burning your hand. Return the skillet to medium heat and add the diced onion with the remaining 0.25 teaspoon of kosher salt. Cook the onion for 3 minutes, stirring with a wooden spoon every 30 seconds, until the pieces are translucent and their raw bite has softened. Add the minced jalapeño and stir for 1 more minute until the jalapeño softens and its bright green color deepens slightly. Remove the skillet from the heat and fold the onion and jalapeño into the sliced chicken in a mixing bowl.
Assemble the Quesadillas: Lay one flour tortilla flat on the cutting board. Scatter 50g / 1.75oz of shredded Monterey Jack cheese across the entire surface of the tortilla in an even layer, stopping 1cm / 0.4in from the edge. Spoon one-quarter of the chicken and aromatic mixture over the cheese on one half of the tortilla only. Fold the empty cheese half over the filled half to form a half-moon shape and press firmly with your palm so the two layers bond. Repeat this assembly process with the remaining 3 tortillas.
Toast the First Quesadilla: Return the skillet to medium heat and add 0.75 teaspoon of unsalted butter. Once the butter melts and begins to foam, slide one assembled quesadilla into the skillet. Press down firmly with the wide flat spatula for 10 seconds to maximize contact between the tortilla and the pan surface. Cook for 3 minutes without lifting the quesadilla until the bottom tortilla is deep golden brown and the cheese nearest the edges begins to melt visibly. Carefully flip the quesadilla using the spatula and cook for 2 minutes on the second side until that surface is equally golden and the cheese inside has fully melted into a cohesive layer.
Finish and Slice: Transfer the finished quesadilla to a wire rack set over a baking sheet rather than a plate, which prevents steam from softening the bottom crust. Repeat step 6 with the remaining 3 quesadillas, adding 0.75 teaspoon of fresh butter to the skillet before each one. Once all four quesadillas are cooked, place each on the cutting board and cut each one into 3 equal wedges using a sharp chef's knife or pizza wheel. Serve immediately while the cheese is molten and the crust retains its crunch.
