Pound boneless chicken breast with meat mallet until 1/4 inch thin, lightly brush on both sides with olive oil and season with salt & pepper. Put on hot grill for 2-3 minutes on each side, slice in thin strips. Set aside.
Preheat grill or skillet pan to medium heat. Place tortillas on a flat surface and divide the Queso Blanco with Chiles and Epazote, Queso Oaxaca, pimento, and basil among the tortillas. Top half of each tortilla with a single layer of sliced chicken and cayenne and fold in half.
Transfer tortillas to pan and grill until they start to brown and crisp. Flip and continue grilling until cheese is melted and second side is crisp.