In a saucepan, melt butter over medium heat. Add flour and mix. Then add the salsa verde and whisk together until well combined.
When it starts to thicken, add the two cups of chicken broth and continue to whisk over medium heat for a couple of minutes.
Add the heavy cream and remove from heat.
Season the shredded chicken with salt, chili powder, cumin, lime and honey. Mix together.
Layer tortillas with chicken, then cheese. Roll them up.
In a 9x13 inch baking pan, pour in half of the sauce. Set the rolled up enchiladas inside, then pour out and spread the other half of the sauce on the enchiladas. Sprinkle with the remaining cheese.
Bake at 400° F for 15-20 minutes, uncovered. Serve immediately!