Wash the brussel sprouts and remove any loose leaves. Trip the stem ends if needed and if leaving them whole, make a small cross-cut in the stem. If you have rather large sprouts, cut them in halves or quarters.
Slice the shallot very thin. Cut the zucchini into slices.
Heat the pan with the olive oil and shallots, and sauté over a medium-low heat until the shallots are wilted. Turn up the heat and toss in the sprouts.
Cook for a couple of minutes then add the zucchini.
Sauté until the sprouts are a very bright green and tender-crunchy, and the zucchini is just a bit limp. Maximum cooking time should be around 10 minutes - any more and you'll bring out that bitter cabbage-iness of the sprouts.