In a mixing bowl, incorporate the flour and butter with a fork.
Place the poblanos, onion, tomatillos, garlic, chicken stock, cream, and milk in a pan and bring to a boil. Whisk in the flour and butter mixture and continue to whisk until all lumps disappear. Cook over medium heat until the mixture thickens.
Add the spinach, asiago cheese, cilantro, and continue to cook for 30 seconds, while stirring. Transfer to a blender in batches, and blend until completely smooth. Strain through a medium strainer back into the heavy pan, season with salt and pepper, and keep warm.
Ladle the soup into warm bowls and garish with tortilla strips and Pico de Gallo, if desired.