In a large skillet over medium heat, warm the olive oil. Add onion and stir to coat. Saute, stirring occasionally, for about 5 minutes or until onion is nicely softened. Do not let the onion brown.
Fold in chicken. Sprinkle with cumin, chili powder, cinnamon, garlic powder, and nutmeg, and fold to incorporate. Stir in water and let simmer, stirring occasionally.
When water is no longer present, stir in your desired amount of cheese. One cup will give you a silky texture, nicely flavored with cheddar. Two cups will give a bit more of a chewy-cheesy texture, with a more prominent cheddar flavor. Once cheese has melted, taste test and add salt and pepper as desired.
While chicken is simmering, toss diced apples with a teaspoon or two of orange juice, just enough to coat the apple pieces. This will keep the apples from browning, plus add a nice fresh tangy flavor.
Serve with small tortillas, plus any additional condiments that you like.