Lightly grease a 9x13 inch casserole or gratin dish.
Add a teaspoon of oil to a large nonstick skillet over medium high heat, and add in the sausage. Saute until the meat browns and is broken into small bite-size pieces, about 7-8 minutes. Remove the sausage to a bowl and set aside.
Return the pan to the stovetop and add in the additional 2 teaspoons of oil. Add in the onions and cook on a medium low heat until golden brown, about 30 minutes.
Add in the mushrooms and savory, and sauté until the mushrooms begin to brown, about 5 minutes. Then stir in the garlic, and stir for 1 minute before adding the spinach and the cooked sausage. Saute until the spinach begins to wilt. Season with salt, pepper and nutmeg and set aside.
In another bowl, mix together the eggs, milk, mustard and a pinch each of salt and pepper.
Arrange half of the bread into a casserole dish, then add in half of sausage mixture, half of the eggs and half of the Swiss cheese. Repeat with the bread, sausage, eggs and cheese again. Finish with the parmigiano reggiano. Cover and refrigerate for 1 hour or up to overnight.
Preheat oven to 350 F.
Bake uncovered for 40 min or until golden brown. Enjoy warm.