Preheat oven to 425 F. Spray a 9 x 13 baking dish with vegetable oil. In a bowl, mix hash browns and salt. Press into the bottom of the baking dish. Drizzle with melted butter. Baked in preheated oven for 45 minutes.
Squeeze excess moisture out of thawed spinach. Set aside.
In a large skillet, saute mushrooms in olive oil on medium heat until brown. Remove and place in a bowl. Add 1 Tablespoon of olive oil to the pan and saute shallots until soft, 1-2 minutes. Add spinach and heat through.
Put spinach into the bowl with the mushrooms and combine.
Add the wine to the pan and reduce to 1/4 cup.
In a separate bowl, combine the eggs with half and half. Add the thyme and salt and pepper to taste.
Spread mushroom-spinach mixture on top of hash browns. Top with Gruyere cheese.
Evenly pour the egg mixture on top.
Bake at 375 F for about 30 minutes or until golden and egg custard is done.
Let sit at least 5 minutes before serving.
If making the egg mixture and filling ahead of time, bring it to room temperature before baking. (Placing the filling in the microwave for 1-2 minutes and stirring will help it come to room temperature more quickly.)