Preheat the oven to 350 degrees. Spray a 9 x 13 baking dish with cooking spray.
Heat the olive oil in a large skillet over medium high heat. Add the onion and cook for 2-3 minutes. Add in the garlic and beef and saute until the beef has browned and is cooked through, about 7-8 minutes. Remove from heat and drain off the fat.
Add the salt, pepper, and half the cheddar cheese to the beef mixture. Mix well and set aside to cool slightly.
Add half the chicken stock and the peppers (about 1/3 cup) to a blender or food processor. Blend until smooth. Taste and add more peppers if desired.
Add remaining chicken stock and blend until smooth.
In a medium sauce pan melt the butter over medium heat.
Once the butter has melted whisk in the flour and cook for one minute. Slowly whisk in the chicken stock Hatch pepper mixture.
Bring the mixture to a boil then reduce heat to a simmer and simmer for 5-10 minutes or until thickened. Remove from heat and adjust seasonings.
Spread a half cup of the sauce on the bottom of the bakinng dish.
Spoon several tablespoons of the beef mixture into each of the tortillas. Fold in the sides and roll them up. Place them seam side down in the pan.
Pour remaining sauce over top of the enchiladas and sprinkle with remaining cheese.
Bake for 15-20 minutes and enjoy.