Spray a 2-quart square baking dish with nonstick coating. Place 6 slices of bread in bottom of prepared dish; set aside. Drain spinach in a colander. Press back of spoon against spinach to force out excess moisture.
In a large skillet, cook onion in butter or oil over medium heat about 3-4 minutes or until onion is tender. Remove from heat and stir in well-drained spinach and dillweed. Spread spinach mixture over bread and top with 1 cup of the swiss cheese. Arrange remaining bread slices on top.
In a medium mixing bowl, combine eggs, milk, salt, and pepper. Pour egg mixture over layers in baking dish. Using a spatula, lightly press down on layers to moisten bread. Sprinkle remaining cheese on top. Cover with plastic wrap and refrigerate for 2-24 hours.
Remove plastic wrap from baking dish. Bake, uncovered in a 375° oven for 45 minutes or until the center appears set and top is golden brown. Let stand for 10 minutes before serving.
Makes 6 servings.