Heat the oil in a nonstick skillet over medium-high heat. Add the mushrooms and cook, stirring occasionally, until starting to brown, 5 minutes. Add the shallots and saute for another 5 minutes. Add the spinach, Italian seasoning, a large pinch of salt and a pinch of pepper. Cook, stirring, until the spinach is wilted, a few minutes more. Remove from heat and let cool.
Pat the crescent roll dough into a 9-by-13-inch casserole dish.
In a large bowl, mix together the sauteed vegetables, mozzarella, Parmesan and eggs. Pat the mixture into the crescent roll dough.