Fill a stock pot with water and 2 tsp of salt (or you can just add a generous pinch.) Make sure the water tastes relatively salty. Heat the water over high and let it come to a boil while you prepare the other ingredients.
With a knife, cut the broccoli florets off of the stem. Cut the broccoli florets into relatively evenly sized pieces and set aside.
Cut the end off of the broccoli stem. With a peeler or paring knife, peel the broccoli stem until the outer layer is fully removed. We remove this outer layer because its stringy and tough to chew through. That's why broccoli stems aren't usually eaten!
If you have any smaller pieces of the broccoli stem leftover, peel those as well. Slice the stem into evenly sized pieces and set aside.
In a mixing bowl, combine all of the sauce ingredients except for salt and your thickener. (So everything in the ingredient list up to water.)
Taste the sauce to see if you like the flavor. If you are using reduced sodium soy sauce, you'll probably want to add a pinch of salt. If not, you may like it the way it is. This is your chance to taste and adjust. If you want more sweetness, add a little more honey. If you want more saltinesss, add a tiny bit of salt until the sauce tastes perfect for you. If you want more garlic or ginger, add more!
Once the sauce is perfect for you, add the thickener and whisk it into the mixture until fully combined. Set the sauce aside.
Heat a skillet or wok over medium high heat and season with a cooking oil of your choice.
Once the oil is shimmering, add the mushrooms to the pan and sauté for 3-5 minutes, until they turn a slightly darker brown and seem partially cooked.
Blanch the broccoli florets and stem slices by adding them to boiling water and letting them cook for 1-1 1/2 minutes, until bright green. Transfer them from the boiling water to the skillet with the mushrooms and sauté for another 2 minutes or so, until the mushrooms are almost fully tender.
Add the sauce mixture to the pan and let it bubble and reduce as you stir the broccoli and mushrooms around. If your sauce isn't reducing, stop stirring the broccoli and mushrooms and let it bubble for a few seconds. If the sauce isn't bubblng, turn your heat up a bit more until it begins to bubble.
Once the sauce is thickened to your liking and the veggies are fully cooked, remove them from the heat and plate. Top with sliced sallions and red cabbage if using. Serve immediately.