In a large skillet, over medium heat, add oil and saute onion and asparagus pieces until the onion is soft and the asparagus is a bright green color. Remove from heat and set aside.
In a large bowl, whick eggs, milk salt and pepper until smooth. Add cheese and fresh herbs. Add bread cubes and the reserved asparagus/onion mixture. Stir to combine and to coat all the bread cubes with liquid.
Lightly oil or butter a 9x13 inch baking dish. Pour the bread mixture into the dish, pressing down to make it fit if necessary. Let the mixture stand for 10 minutes to settle after placing in the dish.
Bake the pudding at 350 degress until the pudding puffs up, the egg custard is set and the top is golden brown, about 45 minutes to 1 hour.
Cool about 15 minutes before cutting and serving as a side dish or with a side salad for a spring lunch.