Place the bread in a shallow dish. Pour 2½ cups milk over the top. Let soak until the bread has absorbed the milk and become soft, about 30 minutes. Gently press the bread slices to extract the milk into a measuring cup, returning the bread slices to the dish. Set both aside.

While the bread is soaking, trim the asparagus, removing the tough, woody ends. Cut the stalks on the diagonal into thin slivers, each about 2 inches long and x inch thick. Arrange the slivered asparagus on a steamer rack and place over gently boiling water. Cover and steam until barely tender, 2 to 3 minutes. Immediately place the asparagus in a bowl of ice water until cold. Drain and set aside.

Preheat oven to 350° F. Butter a 3-quart dish—a souffle dish works well.

In a bowl, beat together the eggs, salt, pepper and the ½ cup reserved milk (if you did not squeeze enough milk from the bread to equal ½ cup, add additional fresh milk, as needed) until well blended. In the prepared dish, layer one-third of the bread.

Reserving 6 to 8 asparagus slivers aside for garnish, top the bread with half the remaining asparagus and half the mixed herbs. Strew one-third of each of the cheeses over the asparagus and herbs. Repeat the layers, using half the remaining bread, all of the remaining asparagus and herbs and half the remaining cheese. Arrange the remaining bread on top, strew the remaining cheese on top and garnish with the reserved asparagus slivers. Pour the milk-egg mixture over the layers, then dot with the butter pieces.

Bake in the preheated oven until the top is crusty brown and a knife inserted into the middle of the pudding comes out clean, about 45 minutes.

Serve hot or warm.