Broccoli isn't particularly common in the Japanese kitchen, but it's gradually become somewhat popular in home cooking. To be honest, I can't think of many times I've actually eaten it when I've traveled to Japan, but I've certainly seen it at supermarkets and department stores.
The few broccoli dishes I've seen in American Japanese restaurants seem oddly unbalanced, overcooked, and out-of-place.
However, the ingredient can be very suitable for aemono or ohitashi. I might even be swayed to blanch it, mince it finely and use it in tamago-yaki.
Broccoli no toufu ae
This side dish, slightly strongly seasoned even for aemono, is made with a blend of soft tofu, toasted, crushed white sesame seeds, sugar, salt, and the tiniest splash of soy sauce.
The broccoli, blanched for about 90 seconds, yields, but still has bite. Once mixed with the ae components, it acquires a savory, juicy character. The flavors play very nicely together.
For a little color and slightly capricious flavor highlight, I also added a little sprinkling of yuzu-shichimi once the aemono was on the plate. Because I used only a tiny touch of this, each bite holds the potential of a little surprise, but the heat from the shichimi doesn't overwhelm the dish.