Day-old rice works dramatically better than fresh — cold rice fries instead of clumps. If using fresh, spread it on a sheet pan and refrigerate for 1 hour minimum.
Slice mushrooms. Mince garlic.
Heat a wok or large skillet over the highest heat your stove allows. Add sesame oil.
Add mushrooms and don't stir for 2 minutes until browned. Stir and cook 2 minutes more. Season with salt. Remove to a plate.
Add olive oil to the wok. Add garlic and cook 30 seconds.
Add cold rice and press flat against the pan. Let sit 2 minutes undisturbed to develop a crust. Toss and repeat once more.
Push rice to edges. Crack eggs into the center, scramble, then fold into the rice before fully set.
Return mushrooms to wok. Add soy sauce and sesame oil. Toss everything together over high heat for 1 minute. Serve immediately.