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Growing on grass (where water is present, as Arizona is extremely dry), drumstick shape when young, and peeling of the brown universal veil all suggest to me a premature C. molybdites. I've seen it in Glendale before: http://www.projectnoah.org/spottings/739.... These are young as well, but a bit older than yours (a mature mushroom of this species looks imposing -- the largest it can get is about 25 cm tall and 40 cm wide!). Best to keep away from them -- they're poisonous.
your pictures don't match when enlarged. Where was it found and growing on what material?