Dice the onion finely and mince the garlic, setting them aside. In your crockpot, combine the chicken breasts, diced onion, minced garlic, tomatoes and chilis, and taco seasoning. Stir well to coat the chicken evenly with the seasoning. This prep work takes just a few minutes and ensures the flavors will distribute evenly during the long, slow cook.
Cover the crockpot and cook on low for 6–8 hours, or on high for 3–4 hours if you're short on time. The chicken is done when it shreds easily with a fork and the flavors have melded together. I prefer the low setting because it keeps the chicken incredibly tender and allows the spices to develop deeper flavor.
Remove the chicken breasts from the crockpot and place them on a cutting board. Using two forks or your hands (they're easiest), shred the chicken into bite-sized pieces. Return the shredded chicken to the crockpot and stir to combine with the sauce. Chop the fresh cilantro and fold it into the mixture just before assembling the quesadillas to keep its bright flavor from fading.
Lay out a tortilla and spoon about 1/3 cup of the chicken mixture onto one half, leaving a half-inch border. Sprinkle roughly 1/3 cup of shredded jack cheese over the filling, then fold the tortilla in half to create a half-moon shape. I find that not overstuffing the quesadillas makes them much easier to flip and ensures they cook evenly on both sides.
Heat a large griddle or skillet over medium-high heat until hot. Working in batches if needed, place the assembled quesadillas on the hot surface and cook for 2–3 minutes until the bottom is golden brown and the cheese begins to melt. Flip carefully and cook the other side for another 2–3 minutes until equally golden. The cheese should be melted throughout and the tortilla crispy.
Transfer the warm quesadillas to a serving plate or individual plates. Let them cool for just a minute to avoid burning your mouth, then serve immediately while the cheese is still warm and gooey.