To a dutch oven, or other large pot, add the olive oil and heat over medium heat. When the oil's hot, add the apples and onion. Stir. Add in the chili powder and cumin, stirring to combine. Cook, stirring occasionally, 6-8 minutes, or until the apples and onions are soft. Transfer them to a plate, and set aside.
Reduce the heat to medium low. Melt the butter in the pot, then whisk in the flour. Let cook for 60 seconds, to let the flour taste cook out.
Add in the broth, whisking in a bit at a time, until the mixture comes back together. Then whisk in the milk. Continue simmering, whisking occasionally, until the mixture's thickened- about 3-5 minutes.
Stir in the chicken and apple/onion mixture until evenly combined.
Stir the chili, if too thick- add a little extra broth to thin it out, otherwise, stir in the cheese until melted. This chili is meant to be on the thicker side.
Serve with your favorite toppings!