Cook wild rice ahead of time according to the instructions on the package. Drain any excess water from the rice.
Preheat oven to 350 degrees
In a large bowl, stir together eggs, milk, seasonings, ham, onions, and asparagus. Make sure to beat eggs well.
Spray a casserole dish with cooking spray
Pour the egg mixture into the casserole dish. Stir in rice and cheese. Make sure there aren't clumps of rice in the dish.
Slice butter into skinny slices and arrange it on top of the casserole. If you're using olive oil, drizzle it on top
Cook in the oven, uncovered for 30-35 minutes. Remove from the oven when it is clear that the eggs are cooked all the way through but still tender.
Remove the baked dish from the oven.
Let the casserole rest for 10 minutes before serving.