Pre-heat oven to 375*. Brush sides and bottom of a 1 1/2 quart casserole dish with softened butter.
In a large mixing bowl, whisk together milk, cream, eggs, salt and pepper, and set aside.
Cut asiago bread into 1/4" slices. Start assembly of the strata by placing one slice of bread on the bottom of the dish. Sprinkle about 1/2 tsp shredded asiago cheese on the bread slice. Cover with another slice of bread and sprinkle the same amount of cheese on top.
Continue this pattern for two more slices then pour about one third of the custard on top. Return to building the strata for four more layers, then pour another third of the custard on. Build the strata until you have reached 1/4 inch from the top of the dish and finish off with remaining custard. Cover the strata and refridgerate 15 minute.
Place the strata dish on a cookie sheet to catch any drips. Bake for about 45 min on the center rack of the oven. The custard should develop a rich, dark color and rise slightly from the pan. (It will settle back after removal from the oven.) Carefully remove from the oven and set aside to cool for about 15 minutes before unmolding.
Carefully invert the strata by placing a 10 inch plate over the top of the dish. Slowly flip the plate and dish over together. Place on the counter and allow the strata to fall from the dish onto the plate. If the strata does not release from the dish, cut around the sides of the dish and try to invert again. Serve hot or warm as an accompaniment with meat and vegetables to fill out the meal.