Make the dressing. Place the cilantro, jalapeno, garlic, pepitas, vinegar, Parmesan cheese, and mayo in a blender. Pulse to puree. If necessary, drizzle in a little water to get it to a pour-able consistency. Taste for seasoning and add salt and pepper.
Toss the chicken breast in about ½ cup of the dressing. Add more if necessary to evenly coat the chicken. Set aside and reserve the remaining dressing for another use.
Sliver the corn tortillas. Heat the olive oil in a medium skillet over medium high heat. When it begins to shimmer, add the tortilla strips and cook until crisp and golden brown, 3-4 minutes. Drain on paper towels.
Place the lettuce leaves on a platter. Top with chicken, avocado and finally the tortilla strips. Serve immediately.