Butter a small 4-cup/960-ml ovenproof baking dish.
Remove the crusts from the bread and cut into slices; you should have about 3 cups.
Lay the slices across the baking dish, slightly overlapping and allowing some edges to hang over the sides.
Whisk together the eggs and milk in a large bowl. Stir in half of the cheese and season with salt and pepper.
Pour three-fourths of the egg mixture over the bread cubes.
Peel the bottom half of the asparagus and break off the stem ends where it snaps naturally. Discard any woody stems.
Layer the mortadella over the bread and top with asparagus spears.
Pour the remaining egg mixture over the top and finish with the remaining cheese. At this point, you can bake the strata immediately, or cover with plastic wrap/cling film and refrigerate overnight for a surprise breakfast in bed.
Bake the strata until just set, 30 to 35 minutes.
Let cool slightly, sprinkle the top with chopped chives, and serve in the baking dish.
P.S. Double this recipe easily for a large crowd, and watch it disappear at every New Year's Brunch or potluck.