To make the sauce, combine chicken broth, tomatillos, chilies, Poblano pepper, onion, green onion, cilantro, lime juice, sugar, cumin, salt, and pepper in large blender. Blend until smooth. Pour into a small nonreactive (stainless steesaucepan and heat over medium high heat. Once it comes to a boil, reduce to medium low and simmer for 20 minutes. Once thickened, remove from heat.
In a medium bowl, whisk together honey, lime juice, chili powder, garlic powder, and salt. Add the shredded chicken, tossing to coat. Cover and refrigerate at least 30 minutes.
In another medium bowl, stir together green enchilada sauce and heavy cream.
Preheat oven to 350 degrees Pour enough sauce, about 1/2 cup each, into a 9x13 and 8x8 baking dish to coat the bottom.
Place a line of chicken on the edge of a flour tortilla. Sprinkle with cheese. Roll the tortilla up and place seam side down in prepared baking dish. Repeat with remaining tortillas and chicken. Pour sauce over tortillas in baking dish and cover with remaining cheese.
Cover dish with foil and bake in preheated oven for 30 minutes. Remove foil and bake 5 minutes until cheese is bubbly and golden.
Let rest 5 minutes, then serve with cilantro and green onions.