Add pulled chicken and enchilada sauce, and cumin to a large bowl. Toss until combined. Season with salt and pepper.
Add chicken to half of the tortilla. Sprinkle with cheese. Fold the other half of the tortilla over.
Heat a large non-stick sauté pan or griddle to a medium-high heat. Cook quesadillas until golden brown and cheese is melted, about 2-3 minutes per side. Cut into wedges andn top with sour cream, lettuce, black olive cheese and tomatoes.