4 ounces (half a bunch) asparagus spears, trimmed and cut into 2-inch pieces
4 1/2 cups day old brioche or croissants, cut into 1 inch cubes
2 cups shredded gruyere or comte cheese
1/2 cup chopped shallots
8 ounces cooked ham, diced
1 1/2 cups half and half
Bring a large pot of salted water to boiling. Add asparagus; cook 5 minutes or until bright green. Shock asparagus in a bowl of ice water to avoid overcooking.
In a 3-quart baking dish spread half of the bread cubes. Top with cheese, shallots, and half the ham and asparagus. Top mixture with remaining bread.
In a bowl whisk together four of the eggs and the half and half. Evenly pour over layers in dish. With a wooden spoon, press down bread pieces into the egg milk mixture to let it absorb. Top with remaining ham and asparagus. Cover; refrigerate until ready to bake.
Preheat oven to 325 degrees. Bake, uncovered, for 30 minutes until slightly golden. With the back of a wooden spoon, press 6 indentations in the top of strata. Pour a whole egg into each indentation. Bake 25 minutes more or until the egg whites are cooked through. Cut into squares to serve.