Place a large (16") cast-iron skillet over medium heat. In a large bowl, mix the pico de gallo (or salsa), cooked meat, cilantro (if using), and cheeses. Spread 1 cup of the mixture onto one half of a flour tortilla, spreading evenly and leaving ½" inch of space between the filling and the outer edge of the tortilla. Fold the other half of the tortilla over the filling and press down evenly. Repeat with the remaining tortillas.
Pour a small amount (~1 tsp.) of olive oil onto a bunched up paper towel; lightly brush the olive oil onto the top of each quesadilla, adding more oil to the towel as needed.
Place two quesadillas in the skillet, oiled side down. Apply olive oil (as before) to the other side of the quesadillas. Cook, covered, until golden-brown on the bottom, 2-4 minutes. Carefully flip the quesadillas and repeat on the other side. Remove the quesadillas to a cutting board and repeat with the remaining quesadillas.
Cut each quesadilla into three equal triangles and serve.