In a large skillet, brown the chicken in the oil and butter. Season with salt and pepper. Set aside on a plate.
In the same skillet, soften the peppers, onions, and garlic for about 5 minutes. Add butter, if needed. Season with salt and pepper. Add the tomatoes and spices and cook for 2 minutes. Remove the skillet from the heat. Return the chicken to the skillet. Add the hummus and yogurt and stir to combine. Adjust the seasoning.
With the rack in the middle position, preheat the oven’s broiler.
Place the naan bread on two baking sheet. Place the chicken mixture on the bread and sprinkle with the cheese. Bake for about 5 minutes or until the cheese is lightly golden brown.