
In a large bowl, whisk together milk, eggs, Dijon and nutmeg; season with salt and pepper, to taste; set aside.
Melt butter in a 12-inch oven-proof skillet over medium-high heat. Stir garlic, green onions and spinach until heated through, about 3-5 minutes. Remove from heat.
Stir in bread cubes and gently toss to combine. Pour milk mixture evenly over the top. Stir in 1/2 cup Swiss, 1/2 cup Gruyere, and 2 tablespoons Parmesan.
Cover and place in the refrigerator for at least 8 hours or overnight.
Preheat oven to 375 degrees F. Remove strata from the refrigerator, let sit for 30 minutes.
Sprinkle with remaining 1/4 cup Swiss, 1/4 cup Gruyere and 2 tablespoons Parmesan.
Place into oven and bake for 25-30 minutes, or until puffed, golden brown and cooked through.
Serve immediately.