Preheat oven to 350 F. Grease a 9x13-inch baking dish.
Heat vegetable oil in a large skillet over medium-low heat.
Add onion, and cook for 2-3 minutes.
Stir in chicken, green chiles, paprika, chile powder, and 1/2 cup chicken broth.
In a separate saucepan, melt butter.
Whisk in flour, and cook for 1 minute.
Stir in half-and-half, Greek yogurt, cream cheese, and remaining 1 ½ cups chicken broth.
Whisk in 1 ½ cups shredded cheese until melted.
Season with salt and pepper to taste.
To assemble, spoon chicken mixture down center of each tortilla.
Roll tortillas up, and place seam side down in prepared baking dish.
Pour cheese mixture all over the top of the enchiladas.
Sprinkle with remaining 1/2 cup Monterrey Jack.
Cover with greased foil, and bake for 15 minutes.
Remove foil, and continue baking for 15-20 more minutes, or until hot, bubbly, and very lightly browned at the edges.
Top with chopped cilantro and crumbled queso fresco just before serving.
Notes
Green chiles: You can use mild, medium, or hot depending on how much heat you'd like to have.
Chicken: You can either poach and shred chicken breast, or you can use leftover cooked chicken breast. You can also use a rotisserie chicken for the shredded chicken.
Ancho chile powder: This type of chile powder is a milder, smokier chile powder. You can use regular chili powder if you prefer.
Chicken broth: I like to use reduced-sodium chicken broth. Feel free to use no salt or regular if you would like.
Half-and-half: Regular or fat-free will work.
Greek yogurt: You can use regular or low-fat sour cream or non-fat, 2%, or whole milk plain Greek yogurt. I don't recommend using fat-free sour cream.
Cream cheese: Regular or reduced-fat will work. I don't recommend using fat-free cream cheese.
Cheese: You can use a similar cheese like Jack or White Cheddar if you prefer. Also, feel free to use more (or less) to taste.
Tortillas: You can use a light or carb-balance flour tortilla in this recipe.