Place the squash into a saucepan, cover with water, and bring to a boil. Simmer the squash until very tender, 15 to 20 minutes. Drain excess water. Cooked squash should equal 2 cups.
Heat olive oil and butter in a skillet over medium-low heat, and cook the onion, garlic, and apple, stirring frequently, until softened and brown, about 15 minutes. Add butternut squash and chicken broth, and bring to a boil over medium heat. Reduce heat just to a simmer, and stir in the milk and cheese blend. Stir until the cheese has melted and the sauce has reached desired thickness, 5 to 10 minutes. Season to taste with salt and black pepper.