In a large skillet over medium-high heat, add 1 Tablespoon of sesame oil, Then add venison steak and brown for 3 minutes per side. Remove from heat, and transfer to a cutting board to let it rest.
In the same skillet over medium-high heat, sauté the mushrooms and asparagus for about 4 minutes, stirring often.
In a 3 to 4-quart saucepan, add chicken broth, mushrooms, bamboo shoots, soy sauce, rice wine vinegar, chili garlic sauce, and ginger. Bring to a boil, then immediately turn down heat and simmer for 5 minutes.
In a small mixing bowl, combine cornstarch and ¼ cup water and blend well. Add cornstarch mixture, cooked mushrooms, and asparagus to broth and simmer for another 2 minutes.
Meanwhile, use a sharp knife to slice the venison steak diagonally against the grain into ¼-inch-thick slices.
Stir soup in a circular motion, then drizzle in the beaten eggs in a thin stream to create ribbons. Add venison steak slices and remaining 1 Tablespoon of sesame oil. Serve immediately.