Start by cutting the broccoli into small, bite-sized florets and set a pot of water to boil. Blanch the broccoli for about 1 minute until it turns bright green and is just starting to soften, then drain and set aside.
Slice the mushrooms thinly, aiming for an even cut to ensure they brown nicely. Mince the garlic and grate or slice the ginger thin for quick release of flavor.
Heat the neutral oil in a wide skillet or wok over high heat until it shimmers and just begins to ripple. Add the minced garlic and ginger, sizzling for about 15 seconds until fragrant and slightly golden.
Add the sliced mushrooms to the pan. Stir quickly and cook for 3-4 minutes until they turn deeply browned and release a nutty aroma, making a crackling sound as they brown.
Toss in the blanched broccoli florets. Stir well to coat with the oil and cook for another 2-3 minutes until the broccoli is bright green with a slight crunch, sizzling gently.
Pour the soy sauce over the vegetables, stirring constantly to evenly coat everything. Continue cooking for about 1 minute until the sauce glazes the ingredients and begins to thicken slightly.
Finish by drizzling a teaspoon of sesame oil over the stir fry. Toss everything together for a final coating, allowing the fragrant aroma to develop as the dish shimmers with a glossy finish.
Remove the stir fry from heat and transfer to a serving plate. Let it sit for a minute to allow flavors to meld, then enjoy hot, with rice or noodles if desired.