Plunge asparagus in boiling water for 2-4 minutes, depending on the thickness of the spears. Drain and rinse immediately with cold water.
Grease a 13 x 9 casserole dish. Layer 6 slices of bread in the bottom of the dish. Top with Swiss cheese.
In a bowl, whisk together eggs, milk and seasonings. Pour into casserole dish. Neatly arrange asparagus spears on top of casserole. Cover and refrigerate at least 30 minutes, or up to 10 hours.
Bake at 350 degrees for 40-45 minutes, until slightly puffed and golden brown around the edges. If the top starts to get brown too quickly, cover with foil for the remaining cooking time. Let sit for 5 minutes before slicing.