Place all tortilla ingredients (except the 1 teaspoon butter used for seasoning the pan) in blender. Blend until smooth, about 20 seconds.
Heat crepe pan or large skillet over high heat. Once hot, add 1 teaspoon butter and coat pan with it. Add about 1/4 cup batter and swirl around to a thin (approximately 6") circle. Cook on first side about 1 minute, then carefully flip. (The first tortilla will stick and be messier; but it will season the pan and the following tortillas will not stick. You'll still need to be careful flipping them.)
Cook remaining tortillas: The first 2-3 can be cooked over high heat. When they start getting too dark too quickly, reduce heat to medium. Continue cooking each one without adding any new fat to the pan. Set aside tortillas as you go, layering them on a plate.
When tortillas are done, assemble chicken filling in medium size bowl: Add chicken, greens of green onions, 1 cup cheddar cheese, 2/3 cup verde salsa, 1/4 cup heavy cream, chèvre or cream cheese, green chilies, oregano, sea salt and cumin. Fold together well.
Grease large casserole dish (9"x13" or similar) and preheat oven to 350 degrees Fahrenheit.
Fill first tortilla with about 1/3-1/2 cup chicken filling. Roll tortilla around filling and place into casserole dish to one side. Continue to fill, roll and place all tortillas into casserole dish until finished.
Pour remaining 1 cup verde salsa evenly over rolled tortillas. Top with remaining 1/2 cup heavy cream and then remaining 2 cups shredded cheddar.
Bake in preheated oven about 30 minutes, until cheese is browned and edges are very bubbly.
Serve with optional toppings/garnishes.