Marinate the chicken thighs - Add the trimmed chicken thighs to a gallon size zip top bag. Pour in the juice from the can of pickled jalapeños. Work the juice around so the chicken is well-coated. Zip the bag up, removing any air from the bag, and marinate in the refrigerator overnight, or at least 6 hours for best results.
Make the jalapeno dressing - Add mayonnaise, sour cream, Spice That seasoning, and pickled jalapeno juice to a medium bowl. Mix together well, cover, and refrigerate until ready to serve.
Season the chicken - When it's done marinating, remove the chicken from the bag, allowing any excess liquid to drip off. Season both sides of each thigh with Fiesta That or your favorite Mexican spice blend.
Prepare the griddle - Preheat griddle to about 375-400℉. Add about 1 tablespoon of high heat cooking oil to the surface, and spread it around with your spatula. *For skillet cooking, heat a large skillet over medium to medium-high heat with 1 tablespoon oil.
Cook the Mexican chicken - Place the chicken thighs top side (smooth side) down on the griddle. Cook untouched about 5-7 minutes on the first side, or until a nice crust develops. Then flip to the second side and cook an additional 5-7 minutes. Continue to cook, flipping a few times so the chicken cooks evenly, until the internal temperature reaches 165℉.
Toast the buns - While the chicken is cooking, slice your bolillo or sandwich rolls in half. Lay the buns cut-side down on the griddle until golden and toasted. *Cover with a dome briefly if you want extra steam and softness.
Add cheese to the chicken - When the thighs reach 165℉, add a slice of pepper jack cheese to each one, and cook until the cheese is melty. Then transfer to a plate to rest for about 5-10 minutes. *You can also cover the thighs with a melting dome to help the cheese melt more quickly.
Assemble the sandwiches - Fan avocado slices on the bottom bun, top with thinly sliced onion and a piece of Mexican chicken. Then drizzle on some of the jalapeno dressing and add the top bun. Serve warm. *If needed, you can add 1-2 tablespoons of milk or half and half to the dressing to thin it out before serving.