Place the oil in a large skillet over medium-high heat and add the onion, garlic and ginger. Saute until the onion is soft and golden, about 4 minutes. Add the coriander seeds, garam masala, paprika, turmeric, and salt and toast for 15 seconds and then add the tomato paste, stirring well to incorporate it. Add the chicken pieces and stir well to coat them the spice mixture and cook until the chicken is almost cooked through, about 8 minutes. Add the yogurt and continue to cook until the chicken is done, about 2 minutes.
Preheat the oven to 400 degrees F.
Place a tortilla on a baking sheet and then cover the surface with some filling. Sprinkle on a third of the cheese and then place another tortilla on top and press it down gently. Brush the top with a bit of oil and then repeat with the remaining tortillas, until 3 quesadillas are assembled. You may need multiple baking sheets. Bake the quesadillas in the preheated oven for about 8 to 10 minutes, or until the cheese is melted and the tortilla is slightly golden. Cut the quesadilla into wedges and serve.