Preheat oven to 400°F. Shred chicken and cheeses. Brush tortillas lightly with olive oil or melted butter and arrange open-faced on a baking sheet.
Layer shredded chicken evenly over each tortilla. Top with a mix of Oaxaca and Monterey Jack cheese. Bake for 5 minutes to melt the cheese slightly.
Remove from oven, fold each tortilla in half, and press gently to seal. Return to oven for another 5 minutes.
Flip tacos, sprinkle cheese on the outside, and broil for about 5 minutes or until golden brown and crisp.
Serve hot with your favorite toppings.