Head vegetable oil in medium (4 quart) pot. Add diced onions and cook for 6-8 minutes until brown.
Add cumin and 2 cloves of pressed garlic and let cook for 30 seconds until aromatic.
Add chicken broth and scrap up any onion bits from bottom of pan and bring it up a simmer (5 minutes)
Add whole chicken breasts to liquid and cover with lid.
Simmer chicken for 15-20 minutes, flipping the breasts over halfway through.
Remove cooked chicken and cover to let rust for 20 minutes. Reserve the chicken broth with softened onion.
Cut peppers in half and remove ribs and seeds. You can leave some ribs and seeds in the jalapeno depending on your desired spice level. Peal and rinse tomatillos, quarter or halve.
Place peppers and tomatillos cut size down on oiled baking sheet and spray tops with cooking oil. Broil until charred and blackened on the top rack. They will look burned but that’s okay. Cool for 10 minutes.
Turn oven to 450F degrees and remove skins from pablano peppers.
Add tomatillos, peppers, salt, sugar and garlic to food processor or blender and blend. Use the reserved liquid to bring to desired consistency. Between 1/4 and 1/3 cup.
Shred the now cooled chicken in a bowl, add 2/3rd of the shredded pepper jack cheese and chopped fresh cilantro. Mix until well blended.
Put 3/4 cup verde sauce in the bottom of a 13 x 9 baking dish and spread evenly.
Oil and bake tortilla on a baking sheet in the oven for 2 minutes to make them soft and pliable.
Using warm tortilla roll 1/3 cup of filling and place seam side down in baking dish.
Pour remaining sauce over top, cover with foil and bake for 15-20 minutes.
Remove from oven. Remove foil and sprinkle with reserved cheese.
