Heat oven to 400 degrees. Coat a shallow 2 1/2 to 3 quart baking dish with olive oil; set aside.
Heat the oil in a large skillet over medium high heat. Add the shallots, 1/2 tsp salt and 1/4 tsp pepper. Cook, stirring occasionally, until soft, 6 to 8 mins. Add the wine and simmer until evaporated, 4 to 6 mins.
Meanwhile, in a large bowl, whisk together the eggs, cream, milk, nutmeg, 1/2 tsp salt and 1/4 tsp pepper.
Squeeze the spinach to remove excess liquid. Stir the spinach, shallots, Guyere, and Parm into the egg mixture. Transfer to the prepared baking dish.
Bake until bubbling and the top is golden brown, 45 to 55 minutes.
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