Prepare a grill fire to about 350° using pecan or hickory for smoke flavor.
Pat chicken tenders dry with paper towels.
Drizzle with olive oil and season with green chile rub on both sides.
Cook chicken tenders over indirect heat with the grill closed 5 minutes.
Flip chicken and continue to cook until chicken reaches 160° using a digital thermometer, about 10 minutes.
Remove chicken from grill to a cutting board. Rest for about 5 minutes and chop coarsely.
Add softened cream cheese to a bowl with shredded cheese and green chile rub.
Add chopped chicken and mix well with a wooded spoon.
Meanwhile, make the enchilada sauce. Add olive oil to a skillet and add flour, whisk together and cook over medium heat for about 2 minutes.
Add chile powders, onion, garlic, cumin, oregano and salt and whisk until combined.
Whisk in chicken broth and tomato sauce, cooking for about 5 minutes.
Add cream, whisk to combine and remove from heat. Cool before assembling enchiladas.
Dip flour tortillas into enchilada sauce and place onto a rimmed dish.
Spoon chicken filling into center of each tortilla.
Roll up enchiladas and place into a baking dish, seam side down.
Repeat with remaining tortillas and filling.
Spoon remaining enchilada sauce over the top.
Cover with foil and place onto the grill.
Cook at 350 - 375° with the grill closed for about 30 minutes.
Remove foil.
Sprinkle enchiladas with shredded cheese and close the grill.
Cook another 10 -15 minutes until cheese is melted.
Remove from grill and cool about 5 minutes.
Garnish with chopped cilantro if desired.
Serve enchiladas with shredded lettuce, tomatoes, onion, salsa and sour cream if desired.