Put oil in a large pot with a lid or a Dutch oven over medium-high heat. When hot, add mushrooms and onion; cook, stirring occasionally, until edges of both brown, about 10 minutes. Add pork, stir, and cook until it begins to brown, 3 to 5 minutes.
Reduce heat to medium and add rice; cook, stirring until combined. Stir in dashi, along with soy sauce and mirin (if using water instead of dashi, add an extra tablespoon soy sauce). Reduce heat so mixture gently bubbles. Cover and cook for 10 minutes.
Uncover. Rice should be almost done and mixture should still be a little soupy (add a bit of dashi or water if dry). Stir in asparagus, then raise heat a bit. Cover and cook until rice and asparagus are just tender and mixture is still moist but not soupy, about 5 to 8 minutes (longer if asparagus is thick). Add salt or more soy sauce to taste if desired. Serve.
Note: Works well with chicken, shrimp, tofu, or even a combination.